| Maximizing the Minimum and Maximum Forcing Numbers of Perfect Matchings of Graphs |
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| 作者姓名： | Qian Qian LIU He Ping ZHANG |
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| 作者单位： | School of Mathematics and Statistics, Lanzhou University |
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| 基金项目： | Supported by National Natural Science Foundation of China (Grant No. 12271229)； |
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| 摘 要： | Let G be a simple graph with 2n vertices and a perfect matching.The forcing number f(G,M) of a perfect matching M of G is the smallest cardinality of a subset of M that is contained in no other perfect matching of G.Among all perfect matchings M of G,the minimum and maximum values of f(G,M) are called the minimum and maximum forcing numbers of G,denoted by f(G) and F(G),respectively.Then f(G)≤F(G) ≤n-1.Che and Chen(2011) proposed an open problem:how to characterize the graphs G with f(G)=n-1.Lat...
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