Disjoint chorded cycles in graphs

Arie Bialostocki, Daniel Finkel, A. Gyárfás

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We propose the following conjecture to generalize results of Pósa and of Corrádi and Hajnal. Let r, s be nonnegative integers and let G be a graph with | V (G) | ≥ 3 r + 4 s and minimal degree δ (G) ≥ 2 r + 3 s. Then G contains a collection of r + s vertex disjoint cycles, s of them with a chord. We prove the conjecture for r = 0, s = 2 and for s = 1. The corresponding extremal problem, to find the minimum number of edges in a graph on n vertices ensuring the existence of two vertex disjoint chorded cycles, is also settled.

Original languageEnglish
Pages (from-to)5886-5890
Number of pages5
JournalDiscrete Mathematics
Volume308
Issue number23
DOIs
Publication statusPublished - Dec 6 2008

Fingerprint

Disjoint
Cycle
Extremal Problems
Graph in graph theory
Chord or secant line
Vertex of a graph
Non-negative
Generalise
Integer

Keywords

  • Cycles
  • Cycles with chords

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Disjoint chorded cycles in graphs. / Bialostocki, Arie; Finkel, Daniel; Gyárfás, A.

In: Discrete Mathematics, Vol. 308, No. 23, 06.12.2008, p. 5886-5890.

Research output: Contribution to journalArticle

Bialostocki, Arie ; Finkel, Daniel ; Gyárfás, A. / Disjoint chorded cycles in graphs. In: Discrete Mathematics. 2008 ; Vol. 308, No. 23. pp. 5886-5890.
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