## Abstract We show that every 3‐connected claw‐free graph which contains no induced copy of __P__~11~ is hamiltonian. Since there exist non‐hamiltonian 3‐connected claw‐free graphs without induced copies of __P__~12~ this result is, in a way, best possible. © 2004 Wiley Periodicals, Inc. J Graph T
Critical graphs for subpancyclicity of 3-connected claw-free graphs
✍ Scribed by Ronald J. Gould; Tomasz Łuczak; Florian Pfender
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 173 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Let ${\cal{F}}_{k}$ be the family of graphs G such that all sufficiently large k ‐connected claw‐free
graphs which contain no induced copies of G are subpancyclic. We show
that for every k≥3 the family ${\cal{F}}_{1}k$ is infinite and make the first step toward the complete characterization of the family ${\cal{F}}_{3}$. © 2009 Wiley Periodicals, Inc. J Graph Theory 62, 263–278, 2009
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