### ANDO KIYOSHI

Emeritus Professor etc. | Emeritus Professor |

- Profile:

Study on discrete mathematics at the Department of Fundamental Sciences of Nippon Medical School.

Study on graph theory, discrete mathematics, algebraic code theory at the University of Electro-Communications

Researcher Information

### Educational Background

Research Activity Information

### Paper

- Minimally contraction-critically 6-connected graphs

Kiyoshi Ando; Shinya Fujita; Ken-ichi Kawarabayashi

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 312, 3, 671-679, Feb. 2012, Peer-reviwed, An edge of a 6-connected graph is said to be removable (resp. contractible) if the removal (resp. contraction) of the edge results in a 6-connected graph. A 6-connected graph is said to be minimally contraction-critically 6-connected if it has neither removable edge nor contractible edge. Let x be a vertex of a minimally contraction-critically 6-connected graph G. In this paper, we show that there is one of some specified configurations around x and using this result we prove that x has a neighbor of degree 6. We also display a condition for x to have at least two neighbors of degree 6. (C) 2011 Published by Elsevier B.V.

Scientific journal, English - The number of vertices of degree 5 in a contraction-critically 5-connected graph

Kiyoshi Ando; Takashi Iwase

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 311, 17, 1925-1939, Sep. 2011, Peer-reviwed, An edge of a 5-connected graph is said to be 5-contractible if the contraction of the edge results in a 5-connected graph. A 5-connected graph with no 5-contractible edge is said to be contraction-critically 5-connected. Let V (G) and V(5)(G) denote the vertex set of a graph G and the set of degree 5 vertices of G, respectively. We prove that each contraction-critically 5-connected graph G has at least vertical bar V(G)vertical bar/2 vertices of degree 5. We also show that there is a sequence of contraction-critically 5-connected graphs {G(i)} such that lim(i ->infinity) vertical bar V(5)(Gi)vertical bar/vertical bar V(G(i))vertical bar = 1/2. (C) 2011 Elsevier B.V. All rights reserved.

Scientific journal, English - Some structural properties of minimally contraction-critically 5-connected graphs

Kiyoshi Ando; Qin Chengfu

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 311, 13, 1084-1097, Jul. 2011, Peer-reviwed, An edge of a k-connected graph is said to be k-removable (resp. k-contractible) if the removal (resp. the contraction) of the edge results in a k-connected graph. A k-connected graph with neither k-removable edge nor k-contractible edge is said to be minimally contraction-critically k-connected. We show that around an edge whose both end vertices have degree greater than 5 of a minimally contraction-critically 5-connected graph, there exists one of two specified configurations. Using this fact, we prove that each minimally contraction-critically 5-connected graph on n vertices has at least 2/3 n vertices of degree 5. (C) 2010 Elsevier B.V. All rights reserved.

Scientific journal, English - Subgraph induced by the set of degree 5 vertices in a contraction critically 5-connected graph

Kiyoshi Ando

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 309, 22, 6359-6367, Nov. 2009, Peer-reviwed, An edge of a 5-connected graph is said to be contractible if the contraction of the edge results in a 5-connected graph. A 5-connected graph with no contractible edge is said to be contraction critically 5-connected. Let G be a contraction critically 5-connected graph and let H be a component of the subgraph induced by the set of degree 5 vertices of G. Then it is known that |V(H)| >= 4. We prove that if |V(H)| = 4, then H congruent to K(4)(-), where K(4)(-) stands for the graph obtained from K(4) by deleting one edge. Moreover, we show that either |N(G)(V(H))| = 5 or |N(G)(V(H))| = 6 and around H there is one of two specified structures called a K(4)(-)-configuration and a split K(4)(-)-configuration. (C) 2008 Elsevier B.V. All rights reserved.

Scientific journal, English - A Local Structure Theorem on 5-Connected Graphs

Kiyoshi Ando

JOURNAL OF GRAPH THEORY, JOHN WILEY & SONS INC, 60, 2, 99-129, Feb. 2009, Peer-reviwed, An edge of a 5-connected graph is said to be contractible if the contraction of the edge results in a 5-connected graph. Let x be a vertex of a 5-connected graph. We prove that if there are no contractible edges whose distance from x is two or less, then either there are two triangles with x in common each of which has a distinct degree five vertex other than x, or there is a specified structure called a K(4)(-)-configuration with center x. As a corollary, we show that if a 5-connected graph on n vertices has no contractible edges, then it has 2n/5 vertices of degree 5. (C) 2008 Wiley Periodicals Inc. J Graph Theory 60: 99-129, 2009

Scientific journal, English - On the number of 4-contractible edges in 4-connected graphs

K. Ando; Y. Egawa; K. Kawarabayashi; Matthias Kriesell

JOURNAL OF COMBINATORIAL THEORY SERIES B, ACADEMIC PRESS INC ELSEVIER SCIENCE, 99, 1, 97-109, Jan. 2009, Peer-reviwed, We prove that every finite 4-connected graph G has at least 1/34 . (|E(G)| - 2|V(G)|) many contractible edges. (C) 2008 Elsevier Inc. All rights reserved.

Scientific journal, English - Edges not contained in triangles and the number of contractible edges in a 4-connected graph

Kiyoshi Ando; Yoshimi Egawa

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 308, 23, 5463-5472, Dec. 2008, Peer-reviwed, Let G be a 4-connected graph, and let E-c(G) denote the set of 4-contractible edges of G and let (E) over bar (G) denote the set of those edges of G which are not contained in a triangle. Under this notation, we show that if vertical bar(E) over bar (G)vertical bar >= 15, then we have vertical bar E-c(G)vertical bar >= (vertical bar(E) over bar (G)vertical bar+8)/4. (C) 2007 Elsevier B.V. All rights reserved.

Scientific journal, English - Edges not contained in triangles and the distribution of contractible edges in a 4-connected graph

Kiyoshi Ando; Yoshimi Egawa

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 308, 16, 3449-3460, Aug. 2008, Peer-reviwed, We prove results concerning the distribution of 4-contractible edges in a 4-connected graph G in connection with the edges of G not contained in a triangle. As a corollary, we show that if G is 4-regular 4-connected graph, then the number of 4-contractible edges of G is at least one half of the number of edges of G not contained in a triangle. (C) 2007 Elsevier B.V. All rights reserved.

Scientific journal, English - Contractible edges in minimally k-connected graphs

Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 308, 4, 597-602, Feb. 2008, Peer-reviwed, An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. In this paper, we prove that a (K-1 + C-4)-free minimally k-connected graph has a k-contractible edge, if incident to each vertex of degree k, there is an edge which is not contained in a triangle. This implies two previous results, one due to Thomassen and the other due to Kawarabayashi. (C) 2007 Elsevier B.V. All rights reserved.

Scientific journal, English - Minimum sets in an A_2-lattice whose component does not induce any equilateral triangle

Kiyoshi Ando; Mamoru Watanabe

The Bulletin of Kurasiki University of Science and the Arts, 12, 1, 105-112, Mar. 2007, Peer-reviwed

Research institution, English - Contractible edges in a k-connected graph

Kiyoshi Ando

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4381, 10-20, 2007, Peer-reviwed, An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. Some results concerning k-contractible edges in a k-connected graph are presented. © 2007 Springer-Verlag Berlin Heidelberg.

International conference proceedings, English - Contractible edges in a 4-connected graph with vertices of degree greater than four

Kiyoshi Ando; Yoshimi Egawa

GRAPHS AND COMBINATORICS, SPRINGER TOKYO, 23, 99-115, 2007, Peer-reviwed, An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. Let G be a 4-connected graph which has a vertex x with degree greater than four. We show that if the subgraph induced by N-G(x) boolean AND V-4(G) is not isomorphic to the path of length three, then there are at least two 4-contractible edges whose distance from x is one or less, where N-G(x) and V-4(G) stand for the neighborhood of x and the set of vertices of G whose degree is 4, respectively. We also show that G has at least vertical bar V->= 5 (G)vertical bar 4-contractible edges.

Scientific journal, English - Contractible edges in a $k$-connected graph

Ando, Kiyoshi

Lecture Notes in Comput. Sci., 4381, 10--20, 2007, Peer-reviwed

Scientific journal, English - Tight quadrangulations on the sphere

H Komuro; K Ando; A Nakamoto

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 306, 2, 278-283, Feb. 2006, Peer-reviwed, A quadrangulation is a simple graph on the sphere each of whose faces is quadrilateral. A quadrangulation G is said to be tight if each edge of G is incident to a vertex of degree exactly 3. We prove that any two tight quadrangulations with n >= 11 vertices, not isomorphic to pseudo double wheels, can be transformed into each other, through only tight quadrangulations, by at most 8/3n -76/3 rhombus rotations. If we restrict quadrangulations to be 3-connected, then the number of rhombus rotations can be decreased to 2n - 22. (c) 2006 Elsevier B.V. All rights reserved.

Scientific journal, English - Trivially noncontractible edges in a contraction critically 5-connected graph

K Ando

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 293, 1-3, 61-72, Apr. 2005, Peer-reviwed, An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is said to be contraction critically k-connected. An edge of a k-connected graph is said to be trivially noncontractible if its end vertices have a common neighbor of degree k. We prove that a contraction critically 5-connected graph on n vertices has at least n/2 trivially noncontractible edges and at least (2n)/9 vertices of degree 5. (c) 2005 Elsevier B.V. All rights reserved.

Scientific journal, English - Vertices of degree 5 in a contraction critically 5-connected graph

K Ando; A Kaneko; K Kawarabayashi

GRAPHS AND COMBINATORICS, SPRINGER TOKYO, 21, 1, 27-37, Mar. 2005, Peer-reviwed, An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is said to be contraction critically k-connected. We prove that a contraction critically 5-connected graph on n vertices has at least n/5 vertices of degree 5. We also show that, for a graph G and an integer k greater than 4, there exists a contraction critically k-connected graph which has G as its induced subgraph.

Scientific journal, English - Vertices of degree 6 in a contraction critically 6-connected graph

K Ando; A Kaneko; K Kawarabayashi

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 273, 1-3, 55-69, Dec. 2003, Peer-reviwed, An edge of a 6-connected graph is said to be 6-contractible if the contraction of the edge results in a 6-connected graph. A contraction critically 6-connected graph is a 6-connected graph with no 6-contractible edge. We prove that each contraction critically 6-connected graph G has at least 1/7\V(G)\ vertices of degree 6. (C) 2003 Elsevier B.V. All rights reserved.

Scientific journal, English - Cycles having the same modularity and removable edges in 2-connected graphs

K Ando; M Hagita; A Kaneko; M Kano; K Kawarabayashi; A Saito

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 265, 1-3, 23-30, Apr. 2003, Peer-reviwed, In this paper, we consider 2-connected multigraphs in which every cycle has length congruent to a modulo b (b greater than or equal to 2). We prove that there exists such a multigraph which is homomorphic to a graph with minimum degree at least three only if a = 0, and that there exists such a graph only if a = 0 and b = 2. We also study the distribution of paths whose internal vertices have degree exactly two, and show a relation between these paths and edges in a 2-connected graph whose deletion results in a 2-connected graph. (C) 2002 Elsevier Science B.V. All rights reserved.

Scientific journal, English - Maximum number of edges in a critically $k$-connected graph

Kiyoshi Ando; Yoshimi Egawa

Discrete Mathematics, 260, 1-3, 1--25, 2003, Peer-reviwed

Scientific journal, English - Some forbidden subgraph conditions for a graph to have a k-contractible edge

Kiyoshi Ando; Kenichi Kawrabayashi

Discrete Mathematics, 297, 1-3, 3-11, 2003, Peer-reviwed

Scientific journal, English - Bandwidth of the cartesian product of two connected graphs

T Kojima; K Ando

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 252, 1-3, 227-235, May 2002, Peer-reviwed, The bandwidth B(G) of a graph G is the minimum of the quantity max{\f(x) - f(y)\:xyepsilonE(G)} taken over all injective integer numberings f of G. The cartesian product of two graphs G and H, written as G x H, is the graph with vertex set V(G) x V(H) and with (u(1), v(1)) adjacent to (u(2), v(2)) if either u(1) is adjacent to u(2) in G and v(1) = v(2) or u(1) = u(2) and v(1) is adjacent to V2 in H. In this paper we investigate the bandwidth of the cartesian product of two connected graphs. For a graph G, we denote the diameter of G and the connectivity of G by D(G) and K(G), respectively. Let G and H be two connected graphs. Among other results, we show that if B(H) = kappa(H) and \V(H)\ > 2B(H)D(G) - min{1,D(G) - 1}, then B(G x H) = B(H)\V(G)\. Moreover, the order condition in this result is sharp. (C) 2002 Elsevier Science B.V. All rights reserved.

Scientific journal, English - Path factors in claw-free graphs

Kiyoshi Ando; Yoshimi Egawa; Atsushi Kaneko; Ken-ichi Kawarabayashi; Haruhide Matsuda

Discrete Mathematics, 243, 1-3, 195--200, 2002, Peer-reviwed

Scientific journal, English - On quadrangulations of closed surfaces covered by vertices of degree 3

Kiyoshi Ando; Atsuhiro Nakamoto

Ars Combin., 62, 121--127, 2002, Peer-reviwed

Scientific journal, English - Graph $G$ for which both $G$ and $\overline G$ are contraction critically $k$-connected

Jin Akiyama; Kiyoshi Ando; Yoshimi Egawa

Graphs Combin., 18, 4, 693--708, 2002, Peer-reviwed

Scientific journal, English - Self-complementary graphs with minimum degree two

Kiyoshi Ando; Atsuhiro Nakamoto

Ars Combin., 65, 65--74, 2002, Peer-reviwed

Scientific journal, English - Edge-wide-diameter of graphs with diameter $d$

Toru Kojima; Kiyoshi Ando; Atsushi Kaneko

Ann. Comb., 6, 1, 57--64, 2002, Peer-reviwed

Scientific journal, English - Diagonal flips of pseudo triangulations on the sphere

H Komuro; K Ando

ARS COMBINATORIA, CHARLES BABBAGE RES CTR, 59, 225-239, Apr. 2001, Peer-reviwed, A plane graph is an embedding of a planar graph into the sphere which may have multiple edges and loops. A face of a plane graph is said to he a pseudo triangle if either the boundary of it has three distinct edges or the boundary of it consists of a loop and a pendant edge. A plane pseudo triangulation is a connected plane graph of which each face is a pseudo triangle. If a plane pseudo triangulation has neither a multiple edge nor a loop, then it is a plane triangulation. As a generalization of the diagonal flip of a plane triangulation, the diagonal flip of a plane pseudo triangulation is naturally defined. In this paper we show that any two plane pseudo triangulations of order n can be transformed into each other, up to ambient isotopy, by at most 14n - 64 diagonal flips if n greater than or equal to 7. We also show that or a positive integer n greater than or equal to 5, there are two plane pseudo triangulations with n, vertices such that at least 4n - 15 diagonal flips are needed to transform into each other.

Scientific journal, English - Minimum length of cycles through specified vertices in graphs with wide-diameter at most d

T Kojima; K Ando

ARS COMBINATORIA, CHARLES BABBAGE RES CTR, 58, 245-256, Jan. 2001, . Let k be a positive integer and let G be a graph. For two distinct vertices x, y is an element of V(G), the k-wide-distance d(k)(x, y) between a: and y is the minimum integer l such that there exist k vertex-disjoint (x,y)-paths whose lengths are at most l. We define d(k)(x,x) = 0. The k-wide-diameter d(k) (G) of G is the maximum value of the k-wide-distance between two vertices of C. In this paper we show that if C is a graph with d(k)(G) greater than or equal to 2 (k greater than or equal to 3), then there exists a cycle which contains specified k vertices and has length at most 2(k - 3)(d(k) (G) - 1) + max {3d(k)(C), [18d(k) (G) - 16]/5}.

Scientific journal, English - Diagonal Transformations of Quadrangulations on the Sphere

K. Ando; A. Nakamoto

Japan Conference on Discrete and Computational Geometry '2000, Nov. 2000

English - Some properties of 5-contraction critical graphs

K. Ando; A. Kaneko; K. Kawarabayashi

6th International Conference on Graph Theory（Marseille, France）, Aug. 2000

English - Wide-diameter and minimum length of fan

T Kojima; K Ando

THEORETICAL COMPUTER SCIENCE, ELSEVIER SCIENCE BV, 235, 2, 257-266, Mar. 2000, Let k be a positive integer and let G be a graph with \ V(G)\ greater than or equal to k + 1. For two distinct vertices x,y is an element of V(G), the k-wide-distance between x and y is the minimum l such that there exist k vertex-disjoint (x,y)-paths whose lengths are at most l. The k-wide-diameter d(k)(G) of G is the maximum value of the Ic-wide-distance between two distinct vertices of G. For x(0) is an element of V(G) and k distinct vertices x(1,)x(2),...,x(k) is an element of V(G) - {x(0)}, we define f(k)(x(0),{x(1),x(2),...,x(k)}) to be the minimum I such that there exist k vertex-disjoint paths P-1,P-2,..,P-k, where P-i is an (x(0),x(i))-path of length at most l. We define f(k)(G) to be the maximum value of f(k)(x(0), {x(1),x(2),...,x(k)}) over every x(0) is an element of V(G) and k distinct vertices x(1),x(2),...,x(k) is an element of V(G)- {x(0)}. We study relationships between dk(G) and fk(G). Among other results, we show that if G is a k-connected graph, k greater than or equal to 2, then d(k)(G) - 1 less than or equal to f(k)(G)less than or equal to max{d(k)(G),(k - 1)d(k)(G) - 4k + 7}. (C) 2000 Elsevier Science B.V. All rights reserved.

Scientific journal, English - Contractible edges in k-connected graphs containing no K^-^_4_

K. Ando; A. Kaneko; K. Kawarabayashi

SUT J. Math., 36, 1, 99-103, 2000

English - The number of edges in a graph with edge version wide-diameter 2 or 3, Combinatorics, Graph Theory, and Algorithms

K. Ando; Y. Egawa

Proceedings of the Eighth Quadrennal International Conference on Graph Theory, Combinatorics, Algorithms, and Applications, New Issues Press,, 1, 43-58, 2000

English - Diagonal flips of plane pseudo triangulations

H. Komuro; K. Ando

応用数学合同研究集会報告集, 139-142, Dec. 1999

English - Diagonal flips of plane pseudo triangulations

安藤 清; 小室秀雄

Proc. of Japan Conference on Discrete and Computational Geometry '99, 6-7, Nov. 1999

English - Edge-Wide-diameter of graphs with diameter d

T. Kojima; K. Ando; A. Kaneko

extended abdstract of 8'th Brtish Combi-natorial Conference, 1999

English - The seven graphs whose H-transformations are uniquely determined

K Ando; H Komuro

ARS COMBINATORIA, CHARLES BABBAGE RES CTR, 46, 305-318, Aug. 1997, Peer-reviwed, H-transformation on a simple 3-connected cubic planar graph G is the dual operation of flip flop on the triangulation G* of the plane, where G* denotes the dual graph of G. We determine the seven 3-connected cubic planar graphs whose H-transformations are uniquely determined up to isomorphism.

Scientific journal, English - The minimum number of edges in a vertex diameter-2-critical graph, Discrete Math.

K. Ando; Y. Egawa

Discrete Mathematics, 167-168, 35-63, 1997, Peer-reviwed

Scientific journal, English - A remark on the connectivity of the complement of a 3-connected graph

K Ando; A Kaneko

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 151, 1-3, 39-47, May 1996, Peer-reviwed, A graph G is said to be bi-3-connected if not only G but also its complement (G) over bar are 3-connected and a two-vertex set whose contraction results in a bi-3-connected graph is called a bi-contractible pair of G. We prove that every bi-3-connected graph of order at least 22 has a bi-contractible pair.

Scientific journal, English - The bandwidth of a tree with k-leaves is at most [┣D7K(/)2┫D7]

Kiyoshi Ando; Atsushi Kaneko; Severino Gervacio

Discrete Mathematics, 150, 1-3, 403-406, 1996, Peer-reviwed

Scientific journal, English - An upper bound for orders of certain (k, (]E87C3[))-connected graphs

Kiyoshi Ando

Discrete Math., 135, 1-3, 371-375, 1994, Peer-reviwed

Scientific journal, English - Almost no graph are autographs

Kiyoshi Ando; Katsuhiro Ota

1-11, 1993, Peer-reviwed

International conference proceedings, English - ある種の代数幾何符号の構成と復号の一方法

栗原 正純; 水野弘文; 安藤清

Reports of The Univ. of Electro-Comm., 4, 1, 77-85, 1991, Peer-reviwed

Research institution, Japanese - DISJOINT SUBSETS OF INTEGERS HAVING A CONSTANT SUM

K ANDO; S GERVACIO; M KANO

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 82, 1, 7-11, May 1990, Peer-reviwed

Scientific journal, English - Algebraic-Geometric Codes of Xs : x
^{s}y+y^{s}z+z^{s}x=0

Kiyoshi Ando; Hirobumi Mizuno

Proceedings of 1990 International Sympo. on Infor. Theory & Its App., 1990

International conference proceedings, English - 代数曲線x
^{s}y+y^{s}x+z^{s}x=0上の代数幾何符号

安藤清; 水野弘文

Reports of The Uriv. of electro-Comm., 2, 2, 297-304, 1989, Peer-reviwed

Research institution, Japanese - 符号長とゼータ関数

水野弘文; 安藤清; 池田浩平; 一条孝

Reports of the Uriv. of Electro-Comm., 1, 1, 115-120, 1988, Peer-reviwed

Research institution, Japanese - CRITICALLY (K,K)-CONNECTED GRAPHS

K ANDO; Y USAMI

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 66, 1-2, 15-20, Aug. 1987, Peer-reviwed

Scientific journal, English - GRAPHS-G FOR WHICH G AND GBAR ARE BOTH SEMIDECOMPOSABLE

K ANDO; Y EGAWA; H MIZUNO

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 65, 2, 109-114, Jun. 1987, Peer-reviwed

Scientific journal, English - CONTRACTILE EDGES IN 3-CONNECTED GRAPHS

K ANDO; H ENOMOTO; A SAITO

JOURNAL OF COMBINATORIAL THEORY SERIES B, ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, 42, 1, 87-93, Feb. 1987, Peer-reviwed

Scientific journal, English - The six biconnected graphs

Kiyoshi ando; Hirobumi Mizuno

Journal of Graph Theory, 10, 1, 117-121, 1986, Peer-reviwed

Scientific journal, English - RAO CONJECTURE ON SELF-COMPLEMENTARY GRAPHS WITH K-FACTORS

K ANDO

JOURNAL OF GRAPH THEORY, JOHN WILEY & SONS INC, 9, 1, 119-121, 1985, Peer-reviwed

Scientific journal, English - ECCENTRIC GRAPHS

J AKIYAMA; K ANDO; D AVIS

DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 56, 1, 1-6, 1985, Peer-reviwed

Scientific journal, English - Biconnectedness of Graphs

Kiyoshi Ando; Hirobumi Mizuno

Number Theory and Combinatorics, 37-42, 1985, Peer-reviwed

International conference proceedings, English - Miscellaneous properties of equi-eccentric graphs

Annals of Discrete Mathematics, 20, 1984

Scientific journal, English - Covering decompositions of graphs

京都大学数理解研究所講究録, 534, 1984

Research institution, English - Characterizations and Classifications of biconnected graphs

Annals of Discrete Mathematics, 13, 1982

Scientific journal, English - On Radius Critical Graphs

京都大学数理解析研究所講究録, 471, 1982

Research institution, English - Biconnectedness of graphs-Forbidden subgraphs and unavoidable subgraphs-

Reports of The Univ. of Electro-Comm., 32, 2, 1982

Research institution, English - Miscellaneous Properties of Equi-Eccentric graphs

京都大学数理解析研究所講究録, 427, 1981

Research institution, English - Equi-eccentric graphs with equi-eccentric complements

TRU Math., 17, 1981

Research institution, English - Certain disconnected groups, II

Reports of The Univ. of Electro-Comm., 30, 1, 1979

Research institution, English - Certain disconnedted groups, I

Reports of The Univ. of Electro-Comm., 29, 2, 1978

Research institution, English - Unitary Geometry, II

Kiyoshi Ando; HIrobumi Mizuno

Reports of The Univ. of Electro-Comm., 28, 1, 1977

Research institution, English - Unitary Geometry, III

Kiyoshi Ando; HIrobumi Mizuno

Reports of The Univ. of Electro-Comm., 28, 2, 1977

Research institution, English - Unitary Geometry, I

Kiyoshi Ando; Hirobumi Mizuno

Reports of The University of Electro-Communications, 27, 2, 1976, Peer-reviwed

Research institution, English

### Books and other publications

### Lectures, oral presentations, etc.

- Contractible edges in k-connected graphs

Ando, Kiyoshi

Invited oral presentation, English, The China-Japan Joint Conference on Discrete Geometry, Combinatorics and Graph Theory, Nankai University and Northwestern Polytechnical University, Tianjin, Xi'an (China), International conference

Nov. 2005 - Every 7-contraction critical graph G has $|V(G)|/64$ vertices of degree 7

K.Ando; A.Kaneko; K.Kawarabayashi

Oral presentation, English, 2002日本数学会総会

Mar. 2002 - Vertices of degree 7 in a 7-contraction critical graph

Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi

Oral presentation, English, 応用数学合同研究集会報告集

Dec. 2001 - Vertices of Degree 6 in a 6-contraction Critical Graph

Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi

Oral presentation, English, EuroConference on Combinatorics, Graph Theory and Applications

Sep. 2001 - Minimally 5-contraction critical graphs

K. Ando

Oral presentation, English, 2001日本数学会秋期総合分科会

Sep. 2001 - Graphs G for which both $G$ and $\bar G$ are k-contraction critical

J. Akiyama; K. Ando

Oral presentation, English, 2001日本数学会秋期総合分科会

Sep. 2001 - Vertices of degree 6 in a 6-contraction critical graph

Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi

Oral presentation, English, HORIZONS IN COMBINATORICS A Conference on Graph Theory, Combinatorics and Computing in conjunction with the 16th Annual Shanks Lectures honoring Baylis and Olivia Shanks

May 2001 - The number of vertices of degree 6 in a 6-contraction critical graph

安藤 清

Oral presentation, English, 日本数学会応用数学分科会講演アブストラクト

Mar. 2001 - Vertices of degree 6 in a 6-contraction critical graph

K. Ando; A. Kaneko; K. Kawarabayashi

Oral presentation, English, 応用数学合同研究集会報告集

Dec. 2000 - On k-contractibe edges

K. Ando; A. Kaneko; K. Kawarabayashi

Oral presentation, English, 第12回日本-フランス組合せ論ワークショップ

Oct. 2000 - A property of 5-contraction critical graph

安藤 清

Oral presentation, English, 日本数学会応用数学分科会講演アブストラクト

Sep. 2000 - On k-contractibe edges

安藤 清

Oral presentation, English, 関西グラフ理論セミナー

Jul. 2000 - Contractible edges in minimally k-connected graphs

K. Ando; A. Kaneko; K. Kawarabayashi

Oral presentation, English, Nineth Quadrennal International Conference on Graph Theory, Combinatorics, Algorithms, and Applications（Kalamazoo, Michigan, U.S.A.）

Jun. 2000 - A forbidden subgraph condition for a graph to have a contractible edge

K. Ando; K. Kawarabayashi

Oral presentation, English, Combinatorics 2000（Gaeta, Italy）

May 2000 - Some sufficent conditions for a graph to have a k-contractible edge

安藤 清

Oral presentation, English, 日本数学応用数学分科会講演アブストラクﾄ

Mar. 2000 - Wide-diameter and minimum length of disjoint Menger path system

安藤 清; 小嶋 徹

Oral presentation, English, 日本数学会応用数学分科会講演アブストラクト

Mar. 2000