图的度和与扩圈
Extending Cycles and Degree Sums in Graphs

作者: 王江鲁 , 程建民 :山东师范大学数学科学学院,济南;

关键词: 顶点的度完全圈可扩图Degree of Vertex Extending Cycle

摘要: 本文讨论了两顶点的度和与圈可扩之间的关系,得到了如下结果:设图G的阶 ,如果G中任意一对不相邻的顶点u,v满足 ,则G中任意一个满足 的圈C是可扩的。这里圈C的下界是最好可能的。由此进一步得到,如果G中任意一对不相邻的顶点u,v满足 ,则G是完全圈可扩的。

Abstract: In this paper, we study the relations between degree sums and extending cycles in graphs. The following results is proved. Let G be a graph of order . If for each pair of nonadjacent vertices u,v in , then every cycle C of G with is extendable. By the result,we have that if for each pair of nonadjacent vertices u,v in , then G is fully cycle ex-tendable.

文章引用: 王江鲁 , 程建民 (2011) 图的度和与扩圈。 理论数学, 1, 64-67. doi: 10.12677/pm.2011.12014

参考文献

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[3] O. Ore. Note on Hamilton circuits. The American Mathematical Monthly, 1960, 67: 55.

[4] G. R. T. Hendry. Extending cycles in graphs. Discrete Mathematics, 1990, 85(1): 59-72.

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