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arXiv · 1808.03893

Partitioning a graph into cycles with a specified number of chords

Shuya Chiba·Suyun Jiang·Jin Yan
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Abstract

For a graph $G$, let $\sigma_{2}(G)$ be the minimum degree sum of two non-adjacent vertices in $G$. A chord of a cycle in a graph $G$ is an edge of $G$ joining two non-consecutive vertices of the cycle. In this paper, we prove the following result, which is an extension of a result of Brandt et al. (J. Graph Theory 24 (1997) 165-173) for large graphs: For positive integers $k$ and $c$, there exists an integer $f(k,c)$ such that, if $G$ is a graph of order $n \ge f(k, c)$ and $\sigma_{2}(G) \ge n$, then $G$ can be partitioned into $k$ vertex-disjoint cycles, each of which has at least $c$ chords.

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Shuya Chiba, Suyun Jiang, Jin Yan. 2018-08-12. Partitioning a graph into cycles with a specified number of chords. https://arxiv.org/abs/1808.03893

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