Disjoint chorded cycles of the same length

Guantao Chen, Ronald J. Gould, Kazuhide Hirohata, Katsuhiro Ota, Songling Shan

研究成果: Article査読

2 被引用数 (Scopus)

抄録

Bollobás and Thomason showed that a multigraph of order n and size at least n + c (c ≥ 1) contains a cycle of length at most 2(⌊n/c⌋ + 1) ⌊log2 2c⌋. We show in this paper that a multigraph (with no loop) of order n and minimum degree at least 5 contains a chorded cycle (a cycle with a chord) of length at most 300 log2 n. As an application of this result, we show that a graph of sufficiently large order with minimum degree at least 3k+8 contains k vertex-disjoint chorded cycles of the same length, which is analogous to Verstraëte's result: A graph of sufficiently large order with minimum degree at least 2k contains k vertex-disjoint cycles of the same length.

本文言語English
ページ(範囲)1030-1041
ページ数12
ジャーナルSIAM Journal on Discrete Mathematics
29
2
DOI
出版ステータスPublished - 2015

ASJC Scopus subject areas

  • 数学 (全般)

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