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arXiv · 1511.04356

A refinement of theorems on vertex-disjoint chorded cycles

Theodore Molla·Michael Santana·Elyse Yeager
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Abstract

In 1963, Corrádi and Hajnal settled a conjecture of Erdős by proving that, for all $k \geq 1$, any graph $G$ with $|G| \geq 3k$ and minimum degree at least $2k$ contains $k$ vertex-disjoint cycles. In 2008, Finkel proved that for all $k \geq 1$, any graph $G$ with $|G| \geq 4k$ and minimum degree at least $3k$ contains $k$ vertex-disjoint chorded cycles. Finkel's result was strengthened by Chiba, Fujita, Gao, and Li in 2010, who showed, among other results, that for all $k \geq 1$, any graph $G$ with $|G| \geq 4k$ and minimum Ore-degree at least $6k-1$ contains $k$ vertex-disjoint cycles. We refine this result, characterizing the graphs $G$ with $|G| \geq 4k$ and minimum Ore-degree at least $6k-2$ that do not have $k$ disjoint chorded cycles.

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Theodore Molla, Michael Santana, Elyse Yeager. 2015-11-13. A refinement of theorems on vertex-disjoint chorded cycles. https://arxiv.org/abs/1511.04356

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