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INDEPENDENT-SET-DELETABLE FACTOR-CRITICAL POWER GRAPHS 总被引:3,自引:0,他引:3
原晋江 《数学物理学报(B辑英文版)》2006,26(4):577-584
It is said that a graph G is independent-set-deletable factor-critical (in short, ID-factor-critical), if, for every independent set 7 which has the same parity as |V(G)|, G-I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The k-th power of G, denoted by Gk, is the graph with vertex set V(G) in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G3 and T(G) (the total graph of G) are ID-factor-critical, and G4 (when |V(G)| is even) is strongly IM-extendable; if G is 2-connected, then D2 is ID-factor-critical. 相似文献
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无爪图的导出匹配可扩性 总被引:6,自引:0,他引:6
若图G的一个匹配M也是G的点导出子图,则称M是图G的一个导出匹配.我们称图G是导出匹配可扩的,若它的任何一个导出匹配可以扩充成一个完美匹配,本文我们讨论无爪图的导出匹配可扩性,得出如下结论,并同时指出这些结果是最好可能的.设图G是有2n个顶点的无爪图,1.若图G是最小度大于或等于2 1,则图G是导出匹配可扩的.2.若图G是局部2连通的,则留G是导出匹配可扩的.3.若图G是k正则的且k≥n,则图G是导出匹配可扩的. 相似文献
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目前我们已知的极大导出匹配可扩图只有Kn,n和K2n.为了研究它们是否是仅有的极大导出匹配可扩图,我们考虑了匹配数,导出匹配数,极大导出匹配可扩图以及一个相关的猜想,并得出了若干相关的结果. 相似文献
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导出匹配问题的NP-完全性以及导出匹配可扩问题的CO-NP-完全性 总被引:8,自引:0,他引:8
图G的一个匹配M是导出的,若M是图G的一个导出子图。图G是导邮匹配可扩的(简记IM-可扩的),若图G的任一导出匹配均含于图G的一个完美匹配当中。本文我们将证明如下结果。⑴对无爪图而言,问题“给定图G以及一个正整数r,确定是否存在图G的一个导出匹配M使得M≥r”是NP-完全的。⑵对直径为2的图以及直径为3的偶图,问题“确定一个给定图是否为导出匹配可扩的”是CO-NP完全的;而对完全多部图而言,问题“ 相似文献
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Jianguo Qian 《Graphs and Combinatorics》2006,22(3):391-398
A graph G is called induced matching extendable (shortly, IM-extendable) if every induced matching of G is included in a perfect matching of G. A graph G is called strongly IM-extendable if every spanning supergraph of G is IM-extendable. The k-th power of a graph G, denoted by Gk, is the graph with vertex set V(G) in which two vertices are adjacent if and only if the distance between them in G is at most k.
We obtain the following two results which give positive answers to two conjectures of Yuan.
Result 1. If a connected graph G with |V(G)| even is locally connected, then G2 is strongly IM-extendable.
Result 2. If G is a 2-connected graph with |V(G)| even, then G3 is strongly IM-extendable.
Research Supported by NSFC Fund 10371102. 相似文献
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A graph G is induced matching extendable, shortly IM-extendable, if every induced matching of G is included in a perfect matching of G. For a nonnegative integer k, a graph G is called a k-edge-deletable IM-extendable graph, if, for every F⊆E(G) with |F|=k, G−F is IM-extendable. In this paper, we characterize the k-edge-deletable IM-extendable graphs with minimum number of edges. We show that, for a positive integer k, if G is ak-edge-deletable IM-extendable graph on 2n vertices, then |E(G)|≥(k+2)n; furthermore, the equality holds if and only if either G≅Kk+2,k+2, or k=4r−2 for some integer r≥3 and G≅C5[N2r], where N2r is the empty graph on 2r vertices and C5[N2r] is the graph obtained from C5 by replacing each vertex with a graph isomorphic to N2r. 相似文献
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