Disjoint chorded cycles of the same length

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1030-1041
Number of pages12
JournalSIAM Journal on Discrete Mathematics
Volume29
Issue number2
DOIs
Publication statusPublished - 2015

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Disjoint
Cycle
Minimum Degree
Multigraph
Graph in graph theory
Chord or secant line
Vertex of a graph

Keywords

  • Chorded cycles
  • Cycles
  • Minimum degree

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Disjoint chorded cycles of the same length. / Chen, Guantao; Gould, Ronald J.; Hirohata, Kazuhide; Ota, Katsuhiro; Shan, Songling.

In: SIAM Journal on Discrete Mathematics, Vol. 29, No. 2, 2015, p. 1030-1041.

Research output: Contribution to journalArticle

Chen, G, Gould, RJ, Hirohata, K, Ota, K & Shan, S 2015, 'Disjoint chorded cycles of the same length', SIAM Journal on Discrete Mathematics, vol. 29, no. 2, pp. 1030-1041. https://doi.org/10.1137/130929837
Chen, Guantao ; Gould, Ronald J. ; Hirohata, Kazuhide ; Ota, Katsuhiro ; Shan, Songling. / Disjoint chorded cycles of the same length. In: SIAM Journal on Discrete Mathematics. 2015 ; Vol. 29, No. 2. pp. 1030-1041.
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