共查询到18条相似文献,搜索用时 93 毫秒
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n圈中辐图的团覆盖数和团划分数 总被引:1,自引:0,他引:1
本主要讨论Petersen图的一类推广图-n圈中辐图的团覆盖数和团划分数,由此得出该图的团覆盖数和团划分数相等的结论,同时给出了其在不同情况下的计算公式。 相似文献
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设 G=(V,E) 为简单图,图 G 的每个至少有两个顶点的极大完全子图称为 G 的一个团. 一个顶点子集 S\subseteq V 称为图 G 的团横贯集, 如果 S 与 G 的所有团都相交,即对于 G 的任意的团 C 有 S\cap{V(C)}\neq\emptyset. 图 G 的团横贯数是图 G 的最小团横贯集所含顶点的数目,记为~${\large\tau}_{C}(G)$. 证明了棱柱图的补图(除5-圈外)、非奇圈的圆弧区间图和 Hex-连接图这三类无爪图的团横贯数不超过其阶数的一半. 相似文献
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讨论了可实现布尔矩阵的容度问题.将可实现布尔矩阵看成是无向图,我们证明了可实现布尔矩阵的容度等于其相应无向图的团覆盖数与孤立点数之和,并给出了通过计算容度来计算团覆盖数,以及通过计算团覆盖数来计算容度的算法框架. 相似文献
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关于图的团符号控制数 总被引:2,自引:0,他引:2
引入了图的团符号控制的概念,给出了n阶图G的团符号控制数γks(G)的若干下限,确定了几类特殊图的团符号控制数,并提出了若干未解决的问题和猜想. 相似文献
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A clique coloring of a graph is a coloring of the vertices so that no maximal clique is monochromatic (ignoring isolated vertices). The smallest number of colors in such a coloring is the clique chromatic number. In this paper, we study the asymptotic behavior of the clique chromatic number of the random graph ??(n,p) for a wide range of edge‐probabilities p = p(n). We see that the typical clique chromatic number, as a function of the average degree, forms an intriguing step function. 相似文献
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Let R be a commutative ring and Г(R) be its zero-divisor graph.We com-pletely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one,two,or three.Furthermore,if R≌ Ri × R2 × … Rn (each Ri is local for i =1,2,3,…,n),we also give algebraic characterizations of the ring R when the clique number of r(R) is four. 相似文献
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A clique covering of a simple graph G is a collection of cliques of G covering all the edges of G such that each vertex is contained in at most k cliques. The smallest k for which G admits a clique covering is called the local clique cover number of G and is denoted by lcc(G). Local clique cover number can be viewed as the local counterpart of the clique cover number that is equal to the minimum total number of cliques covering all edges. In this article, several aspects of the local clique covering problem are studied and its relationships to other well‐known problems are discussed. In particular, it is proved that the local clique cover number of every claw‐free graph is at most , where Δ is the maximum degree of the graph and c is a constant. It is also shown that the bound is tight, up to a constant factor. Moreover, regarding a conjecture by Chen et al. (Clique covering the edges of a locally cobipartite graph, Discrete Math 219(1–3)(2000), 17–26), we prove that the clique cover number of every connected claw‐free graph on n vertices with the minimum degree δ, is at most , where c is a constant. 相似文献
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Chudnovsky and Seymour proved that every connected claw-free graph that contains a stable set of size 3 has chromatic number at most twice its clique number. We improve this for small clique size, showing that every claw-free graph with clique number at most 3 is 4-choosable and every claw-free graph with clique number at most 4 is 7-choosable. These bounds are tight. 相似文献
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一个图的Wiener指数是指这个图中所有点对的距离和.Wiener指数在理论化学中有广泛应用. 本文刻画了给定顶点数及特定参数如色数或团数的图中Wiener指数达最小值的图, 同时也刻画了给定顶点数及团数的图中Wiener指数达最大值的图. 相似文献
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We consider the problem of partitioning a graph into cliques of bounded cardinality. The goal is to find a partition that minimizes the sum of clique costs where the cost of a clique is given by a set function on the nodes. We present a general algorithmic solution based on solving the problem variant without the cardinality constraint. We obtain constant factor approximations depending on the solvability of this relaxation for a large class of submodular cost functions which we call value-monotone submodular functions. For special graph classes we give optimal algorithms. 相似文献
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本文用色函数讨论了图G的团图K(G)为奇圈时c(G)≤d(G)成立的一个充分条件和K(G)为简单连通图时c(G)≤d(G)成立的一个充分条件. 相似文献
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Bo-Jr Li 《Discrete Mathematics》2008,308(11):2075-2079
A clique in a graph G is a complete subgraph of G. A clique covering (partition) of G is a collection C of cliques such that each edge of G occurs in at least (exactly) one clique in C. The clique covering (partition) numbercc(G) (cp(G)) of G is the minimum size of a clique covering (partition) of G. This paper gives alternative proofs, using a unified approach, for the results on the clique covering (partition) numbers of line graphs obtained by McGuinness and Rees [On the number of distinct minimal clique partitions and clique covers of a line graph, Discrete Math. 83 (1990) 49-62]. We also employ the proof techniques to give an alternative proof for the De Brujin-Erd?s Theorem. 相似文献