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Disjoint Chorded Cycles in Graphs with High Ore-Degree

In: Discrete Mathematics and Applications

Author

Listed:
  • Alexandr Kostochka

    (University of Illinois at Urbana–Champaign
    Sobolev Institute of Mathematics)

  • Derrek Yager

    (University of Illinois at Urbana–Champaign)

  • Gexin Yu

    (College of William & Mary)

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.

Suggested Citation

  • Alexandr Kostochka & Derrek Yager & Gexin Yu, 2020. "Disjoint Chorded Cycles in Graphs with High Ore-Degree," Springer Optimization and Its Applications, in: Andrei M. Raigorodskii & Michael Th. Rassias (ed.), Discrete Mathematics and Applications, pages 259-304, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-55857-4_11
    DOI: 10.1007/978-3-030-55857-4_11
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