2-connected claw-free chordal graphs are cycle extendable

Deborah Arangno; David E. Brown

2-connected claw-free chordal graphs are cycle extendable

Combinatorics 2016-03-01 v4

Authors: Deborah Arangno , David E. Brown

Abstract

A cycle $C$ of length $k$ in graph $G$ is extendable if there is another cycle $C'$ in $G$ with $V(C) \subset V(C')$ and length $k+1$ . A graph is cycle extendable if every non-Hamiltonian cycle is extendable. In 1990 Hendry conjectured that any Hamiltonian chordal graph (a Hamiltonian graph with no induced cycle of length greater than three) is cycle extendable, and this conjecture has been verified for Hamiltonian chordal graphs which are interval graphs, planar graphs, and split graphs. We prove that any 2-connected claw-free chordal graph is cycle extendable.

Keywords

hamilton cycles graph cycles graph theory

Cite

@article{arxiv.1310.2901,
  title  = {2-connected claw-free chordal graphs are cycle extendable},
  author = {Deborah Arangno and David E. Brown},
  journal= {arXiv preprint arXiv:1310.2901},
  year   = {2016}
}

Comments

This paper has been withdrawn because Dr. Ben Seamone pointed out that the result has been proved by Clark in 1981 (Congr. Numer. 32 (1981) 199 - 204)

2-connected claw-free chordal graphs are cycle extendable

Abstract

Keywords

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