Abstract
In this paper, we consider a general degree sum condition sufficient to imply the existence of k vertex-disjoint chorded cycles in a graph G. Let \(\sigma _t(G)\) be the minimum degree sum of t independent vertices of G. We prove that if G is a graph of sufficiently large order and \(\sigma _t(G)\ge 3kt-t+1\) with \(k\ge 1\), then G contains k vertex-disjoint chorded cycles. We also show that the degree sum condition on \(\sigma _t(G)\) is sharp. To do this, we also investigate graphs without chorded cycles.
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Acknowledgements
The authors would like to thank the referees for their suggestions and comments, and thank Ariel Keller Rorabaugh for the helpful insights she provided. The second author is supported by the Heilbrun Distinguished Emeritus Fellowship from Emory University Emeritus College. The third author is supported by Japan Society for the Promotion of Science KAKENHI Grant Number JP19K03610.
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Elliott, B., Gould, R.J. & Hirohata, K. On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles. Graphs and Combinatorics 36, 1927–1945 (2020). https://doi.org/10.1007/s00373-020-02227-z
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DOI: https://doi.org/10.1007/s00373-020-02227-z