Graphs and Combinatorics

, Volume 33, Issue 1, pp 181–201 | Cite as

A Refinement of Theorems on Vertex-Disjoint Chorded Cycles

Original Paper

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.

Keywords

Disjoint cycles Chorded cycles Minimum degree Ore-degree 

Mathematics Subject Classification

05C35 05C38 05C75 

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Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Department of MathematicsGrand Valley State UniversityAllendaleUSA
  3. 3.Mathematics DepartmentUniversity of British ColumbiaVancouverCanada

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