Abstract
In 1963, Corrádi and Hajnal settled a conjecture of Erdős by proving that, for all \(k \ge 1\), any graph G with \(|G| \ge 3k\) and minimum degree at least 2k contains k vertex-disjoint cycles. In 2008, Finkel proved that for all \(k \ge 1\), any graph G with \(|G| \ge 4k\) 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 \(k \ge 1\), any graph G with \(|G| \ge 4k\) and minimum Ore-degree at least \(6k-1\) contains k vertex-disjoint chorded cycles. We refine this result, characterizing the graphs G with \(|G| \ge 4k\) and minimum Ore-degree at least \(6k-2\) that do not have k vertex-disjoint chorded cycles.
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Acknowledgements
The authors would like to thank Ron Gould, Megan Cream, and Michael Pelsmajer for productive conversations about this problem. We would also like the anonymous referees for their careful reading of this manuscript and many helpful suggestions.
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T. Molla: This author’s research is supported in part by the NSF Grant DMS-1500121.
M. Santana: This author’s research is supported in part by the NSF Grant DMS-1266016 “AGEP-GRS”.
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Molla, T., Santana, M. & Yeager, E. A Refinement of Theorems on Vertex-Disjoint Chorded Cycles. Graphs and Combinatorics 33, 181–201 (2017). https://doi.org/10.1007/s00373-016-1749-0
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DOI: https://doi.org/10.1007/s00373-016-1749-0