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An Ore-type condition for the existence of two disjoint cycles
Information Processing Letters ( IF 0.7 ) Pub Date : 2020-03-31 , DOI: 10.1016/j.ipl.2020.105957
Maoqun Wang , Jianguo Qian

Let n1 and n2 be two integers with n1,n23 and G a graph of order n=n1+n2. As a variation of Ore's degree condition for the existence of Hamilton cycle in G, El-Zahar proved that if δ(G)n12+n22, then G contains two disjoint cycles of length n1 and n2. Recently, Yan et al. considered the problem by extending the degree condition to degree sum condition and proved that if d(u)+d(v)n+4 for any pair of non-adjacent vertices u and v of G, then G contains two disjoint cycles of length n1 and n2. They further asked whether the degree sum condition can be improved to d(u)+d(v)n+2. In this paper, we give a positive answer to this question. Our result also extends El-Zahar's result when n1 and n2 are both odd.



中文翻译:

存在两个不相交循环的Ore型条件

ñ1个ñ2 是两个整数 ñ1个ñ23G的顺序图ñ=ñ1个+ñ2。El-Zahar证明了G中存在Hamilton环的Ore度条件的变化,证明了δGñ1个2+ñ22,则G包含两个长度不相交的周期ñ1个ñ2。最近,Yan等。通过将度数条件扩展到度数和条件来考虑问题,并证明dü+dvñ+4对于任何对不相邻的顶点ùvģ,然后ģ包含长度的两个不相交的周期ñ1个ñ2。他们进一步询问学位总和条件是否可以改善到dü+dvñ+2。在本文中,我们对这个问题给出了肯定的答案。当以下情况时,我们的结果也扩展了El-Zahar的结果ñ1个ñ2 都是奇怪的。

更新日期:2020-03-31
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