Disjoint Chorded Cycles in Graphs with High Ore-Degree

Alexandr Kostochka (), Derrek Yager () and Gexin Yu ()
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Alexandr Kostochka: University of Illinois at Urbana–Champaign
Derrek Yager: University of Illinois at Urbana–Champaign
Gexin Yu: College of William & Mary

A chapter in Discrete Mathematics and Applications, 2020, pp 259-304 from Springer

Abstract: Abstract In 1963, Corrádi and Hajnal proved that for all k ≥ 1, every graph with at least 3k vertices and minimum degree at least 2k has k vertex-disjoint chorded cycles. In 2010, Chiba, Fujita, Gao, and Li proved that for all k ≥ 1, every graph with |G|≥ 4k and minimum Ore-degree at least 6k − 1 contains k (vertex-)disjoint chorded cycles. In 2016, Molla, Santana, and Yeager refined this to characterize all graphs with at least 4k vertices and minimum Ore-degree at least 6k − 2 that do not have k disjoint chorded cycles. We further strengthen this to characterize the graphs with Ore-degree at least 6k − 3 that do not have k disjoint chorded cycles.

Keywords: Cycles; Chorded cycles; Ore-degree; 05C35; 05C38; 05C70; 05D99 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/978-3-030-55857-4_11

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