安藤 清
| 名誉教授・その他関係者 | 名誉教授 |
- プロフィール:
日本医科大学基礎科学教室で離散数学の研究。
電気通信大学では代数的符号理論、グラフ論を主とする離散数学の研究。
研究者情報
研究活動情報
論文
- Minimally contraction-critically 6-connected graphs
Kiyoshi Ando; Shinya Fujita; Ken-ichi Kawarabayashi
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 312巻, 3号, 掲載ページ 671-679, 出版日 2012年02月, 査読付, 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.
研究論文（学術雑誌）, 英語 - The number of vertices of degree 5 in a contraction-critically 5-connected graph
Kiyoshi Ando; Takashi Iwase
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 311巻, 17号, 掲載ページ 1925-1939, 出版日 2011年09月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Some structural properties of minimally contraction-critically 5-connected graphs
Kiyoshi Ando; Qin Chengfu
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 311巻, 13号, 掲載ページ 1084-1097, 出版日 2011年07月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Subgraph induced by the set of degree 5 vertices in a contraction critically 5-connected graph
Kiyoshi Ando
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 309巻, 22号, 掲載ページ 6359-6367, 出版日 2009年11月, 査読付, 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.
研究論文（学術雑誌）, 英語 - A Local Structure Theorem on 5-Connected Graphs
Kiyoshi Ando
JOURNAL OF GRAPH THEORY, JOHN WILEY & SONS INC, 60巻, 2号, 掲載ページ 99-129, 出版日 2009年02月, 査読付, 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
研究論文（学術雑誌）, 英語 - 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巻, 1号, 掲載ページ 97-109, 出版日 2009年01月, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 23号, 掲載ページ 5463-5472, 出版日 2008年12月, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 16号, 掲載ページ 3449-3460, 出版日 2008年08月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Contractible edges in minimally k-connected graphs
Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 308巻, 4号, 掲載ページ 597-602, 出版日 2008年02月, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 1号, 掲載ページ 105-112, 出版日 2007年03月, 査読付
研究論文（大学，研究機関等紀要）, 英語 - 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巻, 掲載ページ 10-20, 出版日 2007年, 査読付, 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.
研究論文（国際会議プロシーディングス）, 英語 - Contractible edges in a 4-connected graph with vertices of degree greater than four
Kiyoshi Ando; Yoshimi Egawa
GRAPHS AND COMBINATORICS, SPRINGER TOKYO, 23巻, 掲載ページ 99-115, 出版日 2007年, 査読付, 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.
研究論文（学術雑誌）, 英語 - Contractible edges in a $k$-connected graph
Ando, Kiyoshi
Lecture Notes in Comput. Sci., 4381巻, 掲載ページ 10--20, 出版日 2007年, 査読付
研究論文（学術雑誌）, 英語 - Tight quadrangulations on the sphere
H Komuro; K Ando; A Nakamoto
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 306巻, 2号, 掲載ページ 278-283, 出版日 2006年02月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Trivially noncontractible edges in a contraction critically 5-connected graph
K Ando
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 293巻, 1-3号, 掲載ページ 61-72, 出版日 2005年04月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Vertices of degree 5 in a contraction critically 5-connected graph
K Ando; A Kaneko; K Kawarabayashi
GRAPHS AND COMBINATORICS, SPRINGER TOKYO, 21巻, 1号, 掲載ページ 27-37, 出版日 2005年03月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Vertices of degree 6 in a contraction critically 6-connected graph
K Ando; A Kaneko; K Kawarabayashi
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 273巻, 1-3号, 掲載ページ 55-69, 出版日 2003年12月, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 1-3号, 掲載ページ 23-30, 出版日 2003年04月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Maximum number of edges in a critically $k$-connected graph
Kiyoshi Ando; Yoshimi Egawa
Discrete Mathematics, 260巻, 1-3号, 掲載ページ 1--25, 出版日 2003年, 査読付
研究論文（学術雑誌）, 英語 - Some forbidden subgraph conditions for a graph to have a k-contractible edge
Kiyoshi Ando; Kenichi Kawrabayashi
Discrete Mathematics, 297巻, 1-3号, 掲載ページ 3-11, 出版日 2003年, 査読付
研究論文（学術雑誌）, 英語 - Bandwidth of the cartesian product of two connected graphs
T Kojima; K Ando
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 252巻, 1-3号, 掲載ページ 227-235, 出版日 2002年05月, 査読付, 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.
研究論文（学術雑誌）, 英語 - Path factors in claw-free graphs
Kiyoshi Ando; Yoshimi Egawa; Atsushi Kaneko; Ken-ichi Kawarabayashi; Haruhide Matsuda
Discrete Mathematics, 243巻, 1-3号, 掲載ページ 195--200, 出版日 2002年, 査読付
研究論文（学術雑誌）, 英語 - On quadrangulations of closed surfaces covered by vertices of degree 3
Kiyoshi Ando; Atsuhiro Nakamoto
Ars Combin., 62巻, 掲載ページ 121--127, 出版日 2002年, 査読付
研究論文（学術雑誌）, 英語 - Graph $G$ for which both $G$ and $\overline G$ are contraction critically $k$-connected
Jin Akiyama; Kiyoshi Ando; Yoshimi Egawa
Graphs Combin., 18巻, 4号, 掲載ページ 693--708, 出版日 2002年, 査読付
研究論文（学術雑誌）, 英語 - Self-complementary graphs with minimum degree two
Kiyoshi Ando; Atsuhiro Nakamoto
Ars Combin., 65巻, 掲載ページ 65--74, 出版日 2002年, 査読付
研究論文（学術雑誌）, 英語 - Edge-wide-diameter of graphs with diameter $d$
Toru Kojima; Kiyoshi Ando; Atsushi Kaneko
Ann. Comb., 6巻, 1号, 掲載ページ 57--64, 出版日 2002年, 査読付
研究論文（学術雑誌）, 英語 - Diagonal flips of pseudo triangulations on the sphere
H Komuro; K Ando
ARS COMBINATORIA, CHARLES BABBAGE RES CTR, 59巻, 掲載ページ 225-239, 出版日 2001年04月, 査読付, 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.
研究論文（学術雑誌）, 英語 - 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巻, 掲載ページ 245-256, 出版日 2001年01月, . 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}.
研究論文（学術雑誌）, 英語 - Diagonal Transformations of Quadrangulations on the Sphere
K. Ando; A. Nakamoto
Japan Conference on Discrete and Computational Geometry '2000, 出版日 2000年11月
英語 - Some properties of 5-contraction critical graphs
K. Ando; A. Kaneko; K. Kawarabayashi
6th International Conference on Graph Theory（Marseille, France）, 出版日 2000年08月
英語 - Wide-diameter and minimum length of fan
T Kojima; K Ando
THEORETICAL COMPUTER SCIENCE, ELSEVIER SCIENCE BV, 235巻, 2号, 掲載ページ 257-266, 出版日 2000年03月, 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.
研究論文（学術雑誌）, 英語 - Contractible edges in k-connected graphs containing no K^-^_4_
K. Ando; A. Kaneko; K. Kawarabayashi
SUT J. Math., 36巻, 1号, 掲載ページ 99-103, 出版日 2000年
英語 - 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巻, 掲載ページ 43-58, 出版日 2000年
英語 - Diagonal flips of plane pseudo triangulations
H. Komuro; K. Ando
応用数学合同研究集会報告集, 掲載ページ 139-142, 出版日 1999年12月
英語 - Diagonal flips of plane pseudo triangulations
安藤 清; 小室秀雄
Proc. of Japan Conference on Discrete and Computational Geometry '99, 掲載ページ 6-7, 出版日 1999年11月
英語 - Edge-Wide-diameter of graphs with diameter d
T. Kojima; K. Ando; A. Kaneko
extended abdstract of 8'th Brtish Combi-natorial Conference, 出版日 1999年
英語 - The seven graphs whose H-transformations are uniquely determined
K Ando; H Komuro
ARS COMBINATORIA, CHARLES BABBAGE RES CTR, 46巻, 掲載ページ 305-318, 出版日 1997年08月, 査読付, 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.
研究論文（学術雑誌）, 英語 - The minimum number of edges in a vertex diameter-2-critical graph, Discrete Math.
K. Ando; Y. Egawa
Discrete Mathematics, 167-168巻, 掲載ページ 35-63, 出版日 1997年, 査読付
研究論文（学術雑誌）, 英語 - A remark on the connectivity of the complement of a 3-connected graph
K Ando; A Kaneko
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 151巻, 1-3号, 掲載ページ 39-47, 出版日 1996年05月, 査読付, 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.
研究論文（学術雑誌）, 英語 - The bandwidth of a tree with k-leaves is at most [┣D7K(/)2┫D7]
Kiyoshi Ando; Atsushi Kaneko; Severino Gervacio
Discrete Mathematics, 150巻, 1-3号, 掲載ページ 403-406, 出版日 1996年, 査読付
研究論文（学術雑誌）, 英語 - An upper bound for orders of certain (k, (]E87C3[))-connected graphs
Kiyoshi Ando
Discrete Math., 135巻, 1-3号, 掲載ページ 371-375, 出版日 1994年, 査読付
研究論文（学術雑誌）, 英語 - ほとんど全てのグラフはautographではない.
Kiyoshi Ando; Katsuhiro Ota
掲載ページ 1-11, 出版日 1993年, 査読付
研究論文（国際会議プロシーディングス）, 英語 - 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
電気通信大学紀要, 4巻, 1号, 掲載ページ 77-85, 出版日 1991年, 査読付
研究論文（大学，研究機関等紀要）, 日本語 - DISJOINT SUBSETS OF INTEGERS HAVING A CONSTANT SUM
K ANDO; S GERVACIO; M KANO
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 82巻, 1号, 掲載ページ 7-11, 出版日 1990年05月, 査読付
研究論文（学術雑誌）, 英語 - Algebraic-Geometric Codes of Xs : xsy+ysz+zsx=0
Kiyoshi Ando; Hirobumi Mizuno
Proceedings of 1990 International Sympo. on Infor. Theory & Its App., 出版日 1990年
研究論文（国際会議プロシーディングス）, 英語 - 代数曲線xsy+ysx+zsx=0上の代数幾何符号
安藤清; 水野弘文
電気通信大学紀要, 2巻, 2号, 掲載ページ 297-304, 出版日 1989年, 査読付
研究論文（大学，研究機関等紀要）, 日本語 - 符号長とゼータ関数
水野弘文; 安藤清; 池田浩平; 一条孝
電気通信大学紀要, 1巻, 1号, 掲載ページ 115-120, 出版日 1988年, 査読付
研究論文（大学，研究機関等紀要）, 日本語 - CRITICALLY (K,K)-CONNECTED GRAPHS
K ANDO; Y USAMI
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 66巻, 1-2号, 掲載ページ 15-20, 出版日 1987年08月, 査読付
研究論文（学術雑誌）, 英語 - Graphs G for which G and G┣D4-┫D4 are both semidecomposable
Koyoshi Ando; Yoshimi Egawa; HIrobumi Mizuno
Discrete Mathematics, ELSEVIER SCIENCE BV, 65巻, 2号, 掲載ページ 109-114, 出版日 1987年06月, 査読付
研究論文（学術雑誌）, 英語 - 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巻, 1号, 掲載ページ 87-93, 出版日 1987年02月, 査読付
研究論文（学術雑誌）, 英語 - The six biconnected graphs
Kiyoshi ando; Hirobumi Mizuno
Journal of Graph Theory, 10巻, 1号, 掲載ページ 117-121, 出版日 1986年, 査読付
研究論文（学術雑誌）, 英語 - RAO CONJECTURE ON SELF-COMPLEMENTARY GRAPHS WITH K-FACTORS
K ANDO
JOURNAL OF GRAPH THEORY, JOHN WILEY & SONS INC, 9巻, 1号, 掲載ページ 119-121, 出版日 1985年, 査読付
研究論文（学術雑誌）, 英語 - ECCENTRIC GRAPHS
J AKIYAMA; K ANDO; D AVIS
DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, 56巻, 1号, 掲載ページ 1-6, 出版日 1985年, 査読付
研究論文（学術雑誌）, 英語 - Biconnectedness of Graphs
Kiyoshi Ando; Hirobumi Mizuno
Number Theory and Combinatorics, 掲載ページ 37-42, 出版日 1985年, 査読付
研究論文（国際会議プロシーディングス）, 英語 - Miscellaneous properties of equi-eccentric graphs
Annals of Discrete Mathematics, 掲載ページ 20, 出版日 1984年
研究論文（学術雑誌）, 英語 - グラフの被覆分解
京都大学数理解研究所講究録, 掲載ページ 534, 出版日 1984年
研究論文（大学，研究機関等紀要）, 英語 - Characterizations and Classifications of biconnected graphs
Annals of Discrete Mathematics, 掲載ページ 13, 出版日 1982年
研究論文（学術雑誌）, 英語 - On Radius Critical Graphs
京都大学数理解析研究所講究録, 掲載ページ 471, 出版日 1982年
研究論文（大学，研究機関等紀要）, 英語 - グラフの双連結性-禁止部分グラフおよび不可避グラフ-
電気通信大学学報, 32巻, 掲載ページ 2, 出版日 1982年
研究論文（大学，研究機関等紀要）, 英語 - Miscellaneous Properties of Equi-Eccentric graphs
京都大学数理解析研究所講究録, 掲載ページ 427, 出版日 1981年
研究論文（大学，研究機関等紀要）, 英語 - Equi-eccentric graphs with equi-eccentric complements
TRU Math., 掲載ページ 17, 出版日 1981年
研究論文（大学，研究機関等紀要）, 英語 - ある種の不連続群,II
電気通信大学学報, 30巻, 掲載ページ 1, 出版日 1979年
研究論文（大学，研究機関等紀要）, 英語 - ある種の不連続群,I
電気通信大学学報, 29巻, 掲載ページ 2, 出版日 1978年
研究論文（大学，研究機関等紀要）, 英語 - ユニタリ幾何(II)
Kiyoshi Ando; HIrobumi Mizuno
電気通信大学学報, 28巻, 掲載ページ 1, 出版日 1977年
研究論文（大学，研究機関等紀要）, 英語 - ユニタリ幾何(III)
Kiyoshi Ando; HIrobumi Mizuno
電気通信大学学報, 28巻, 掲載ページ 2, 出版日 1977年
研究論文（大学，研究機関等紀要）, 英語 - ユニタリ幾何(I)
Kiyoshi Ando; Hirobumi Mizuno
電気通信大学学報, 27巻, 掲載ページ 2, 出版日 1976年, 査読付
研究論文（大学，研究機関等紀要）, 英語
書籍等出版物
講演・口頭発表等
- Contractible edges in k-connected graphs
Ando, Kiyoshi
口頭発表（招待・特別）, 英語, The China-Japan Joint Conference on Discrete Geometry, Combinatorics and Graph Theory, Nankai University and Northwestern Polytechnical University, Tianjin, Xi'an (China), 国際会議
発表日 2005年11月 - Every 7-contraction critical graph G has $|V(G)|/64$ vertices of degree 7
K.Ando; A.Kaneko; K.Kawarabayashi
口頭発表（一般）, 英語, 2002日本数学会総会
発表日 2002年03月 - Vertices of degree 7 in a 7-contraction critical graph
Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi
口頭発表（一般）, 英語, 応用数学合同研究集会報告集
発表日 2001年12月 - Vertices of Degree 6 in a 6-contraction Critical Graph
Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi
口頭発表（一般）, 英語, EuroConference on Combinatorics, Graph Theory and Applications
発表日 2001年09月 - Minimally 5-contraction critical graphs
K. Ando
口頭発表（一般）, 英語, 2001日本数学会秋期総合分科会
発表日 2001年09月 - Graphs G for which both $G$ and $\bar G$ are k-contraction critical
J. Akiyama; K. Ando
口頭発表（一般）, 英語, 2001日本数学会秋期総合分科会
発表日 2001年09月 - Vertices of degree 6 in a 6-contraction critical graph
Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi
口頭発表（一般）, 英語, HORIZONS IN COMBINATORICS A Conference on Graph Theory, Combinatorics and Computing in conjunction with the 16th Annual Shanks Lectures honoring Baylis and Olivia Shanks
発表日 2001年05月 - The number of vertices of degree 6 in a 6-contraction critical graph
安藤 清
口頭発表（一般）, 英語, 日本数学会応用数学分科会講演アブストラクト
発表日 2001年03月 - Vertices of degree 6 in a 6-contraction critical graph
K. Ando; A. Kaneko; K. Kawarabayashi
口頭発表（一般）, 英語, 応用数学合同研究集会報告集
発表日 2000年12月 - On k-contractibe edges
K. Ando; A. Kaneko; K. Kawarabayashi
口頭発表（一般）, 英語, 第12回日本-フランス組合せ論ワークショップ
発表日 2000年10月 - A property of 5-contraction critical graph
安藤 清
口頭発表（一般）, 英語, 日本数学会応用数学分科会講演アブストラクト
発表日 2000年09月 - On k-contractibe edges
安藤 清
口頭発表（一般）, 英語, 関西グラフ理論セミナー
発表日 2000年07月 - Contractible edges in minimally k-connected graphs
K. Ando; A. Kaneko; K. Kawarabayashi
口頭発表（一般）, 英語, Nineth Quadrennal International Conference on Graph Theory, Combinatorics, Algorithms, and Applications（Kalamazoo, Michigan, U.S.A.）
発表日 2000年06月 - A forbidden subgraph condition for a graph to have a contractible edge
K. Ando; K. Kawarabayashi
口頭発表（一般）, 英語, Combinatorics 2000（Gaeta, Italy）
発表日 2000年05月 - Some sufficent conditions for a graph to have a k-contractible edge
安藤 清
口頭発表（一般）, 英語, 日本数学応用数学分科会講演アブストラクﾄ
発表日 2000年03月 - Wide-diameter and minimum length of disjoint Menger path system
安藤 清; 小嶋 徹
口頭発表（一般）, 英語, 日本数学会応用数学分科会講演アブストラクト
発表日 2000年03月