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arXiv · 1705.02819

On degree sum conditions for 2-factors with a prescribed number of cycles

Shuya Chiba
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Abstract

For a vertex subset $X$ of a graph $G$, let $Δ_{t}(X)$ be the maximum value of the degree sums of the subsets of $X$ of size $t$. In this paper, we prove the following result: Let $k$ be a positive integer, and let $G$ be an $m$-connected graph of order $n \ge 5k - 2$. If $Δ_{2}(X) \ge n$ for every independent set $X$ of size $\lceil m/k \rceil+1$ in $G$, then $G$ has a 2-factor with exactly $k$ cycles. This is a common generalization of the results obtained by Brandt et al. [Degree conditions for 2-factors, J. Graph Theory 24 (1997) 165-173] and Yamashita [On degree sum conditions for long cycles and cycles through specified vertices, Discrete Math. 308 (2008) 6584-6587], respectively.

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Shuya Chiba. 2017-06-01. On degree sum conditions for 2-factors with a prescribed number of cycles. https://arxiv.org/abs/1705.02819

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