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A New Characterization of Simple K_3-groups 认领 引用 被引量：2
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作者 王临红 《Northeastern Mathematical Journal》 2001年第2期205-209,共5页
In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorph... In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorphic to M if and only if the set of the orders of the maximal abelian subgoups of G is the same as that of M . 展开更多
关键词 finite group simple K\-3-group maximal abelian subgroup prime graph
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最少边数的n阶3-点连通简单图及其构造 认领 引用
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作者 张秀平 肖旺裕 《北京师范大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第4期339-343,共5页
从图的度数列入手,采用一种特殊的构造方法,不仅得到了3-点连通简单图的最少边数c(G)的值,还得到了图的边数最少时的连通简单图.
关键词 度数列 3-点连通简单图 简单图化 最少边数
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Z3-CONNECTIVITY OF 4-EDGE-CONNECTED TRIANGULAR GRAPHS 认领 引用
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作者 Chuixiang Zhou 《Annals of Applied Mathematics》 2017年第4期428-438,共11页
A graph G is k-triangular if each of its edge is contained in at least k triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph G is a sequen... A graph G is k-triangular if each of its edge is contained in at least k triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph G is a sequence of distinct triangles T1T2%…Tk in G such that for 1 〈 i 〈 k - 1, IE（Ti）∩E（Ti＋1）1= 1 and E（Ti） n E（Tj）=φ if j 〉 i＋1. Two edges e, e＇∈ E（G） are triangularly connected if there is a triangle-path T1, T2,... , Tk in G such that e ∈ E（T1） and er ∈ E（Tk）. Two edges e, e＇ ∈E（G） are equivalent if they are the same, parallel or triangularly connected. It is easy to see that this is an equivalent relation. Each equivalent class is called a triangularly connected component. In this paper, we prove that every 4-edge-connected triangular graph G is Z3-connected, unless it has a triangularly connected component which is not Z3-connected but admits a nowhere-zero 3-flow. 展开更多
关键词 Z3-connected nowhere-zero 3-flow triangular graphs
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Minor and Minimum Cycle Bases of a 3-connected Planar Graph 认领 引用 被引量：1
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作者 Deng Ju MA Han REN 《Acta Mathematica Sinica,English Series》 SCIE 2009年第4期649-656,共8页
In this paper, we prove that if any set of ｜E（G）｜- ｜V（G）｜ ＋ 1 facial cycles of a 3-connected planar graph G embedded in the plane doesn＇t form a minimum cycle base of G, then any minimum cycle base of G cont... In this paper, we prove that if any set of ｜E（G）｜- ｜V（G）｜ ＋ 1 facial cycles of a 3-connected planar graph G embedded in the plane doesn＇t form a minimum cycle base of G, then any minimum cycle base of G contains a separating cycle, and G has a minor isomorphic to T6, where T6 is the graph obtained from the complete graph K6 by deleting a path with four edges. 展开更多
关键词 cycle space minimum cycle base 3-connected planar graph
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Nowhere-zero 3-flows in matroid base graph 认领 引用
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作者 Yinghao ZHANG Guizhen LIU 《Frontiers of Mathematics in China》 SCIE CSCD 2013年第1期217-227,共11页
The base graph of a simple matroid M=(E,A)is the graph G such that V(G)=A and E(G)={BB':B,B'B,[B/B'|=1},where the same notation is used for the vertices of G and the bases of M.It is proved that the base g... The base graph of a simple matroid M=(E,A)is the graph G such that V(G)=A and E(G)={BB':B,B'B,[B/B'|=1},where the same notation is used for the vertices of G and the bases of M.It is proved that the base graph G of connected simple matroid M is Z3-connected if|V(G)|≥5.We also proved that if M is not a connected simple matroid,then the base graph G of M does not admit a nowhere-zero 3-flow if and only if IV(G)[=4.Furthermore,if for every connected component Ei(i≥2)of M,the matroid base graph Gi of Mi=MIEi has IV(Gi)|≥5,then G is Z3-connected which also implies that G admits nowhere-zero 3-flow immediately. 展开更多
关键词 Matroid base graph nowhere-zero 3-flow Z3-connectivity
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Connectivity of Minimum Non-5-injectively Colorable Planar Cubic Graphs 认领 引用
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作者 Jing Jin Bao-Gang Xu 《Journal of the Operations Research Society of China》 EI CSCD 2020年第1期105-116,共12页
Suppose that G is a planar cubic graph withχi(G)>5.We show that ifχi(H)<χi(G)for each planar cubic graph H of order less thanG,thenG is either a 3-connected simple planar cubic graph,or a planar graph obtaine... Suppose that G is a planar cubic graph withχi(G)>5.We show that ifχi(H)<χi(G)for each planar cubic graph H of order less thanG,thenG is either a 3-connected simple planar cubic graph,or a planar graph obtained from a simple cubic 3-connected planar graph by adding some earrings.This shows that a minimum non-5-injectively colorable simple planar cubic graph must be 3-connected. 展开更多
关键词 Planar cubic graphs Connectivity 3-connected Injective coloring
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