### Abstract

Let cl(G) denote Ryjáček's closure of a claw-free graph G. In this article, we prove the following result. Let G be a 4-connected claw-free graph. Assume that G[N _{G}(T)] is cyclically 3-connected if T is a maximal K _{3} in G which is also maximal in cl(G). Then G is hamiltonian. This result is a common generalization of Kaiser et al.'s theorem [J Graph Theory 48(4) (2005), 267-276] and Pfender's theorem [J Graph Theory 49(4) (2005), 262-272].

Original language | English |
---|---|

Pages (from-to) | 40-53 |

Number of pages | 14 |

Journal | Journal of Graph Theory |

Volume | 70 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 May |

### Fingerprint

### Keywords

- claw-free graph
- Hamiltonian cycle
- maximal K

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

**Maximal K _{3}'s and Hamiltonicity of 4-connected claw-free graphs.** / Fujisawa, Jun; Ota, Katsuhiro.

Research output: Contribution to journal › Article

_{3}'s and Hamiltonicity of 4-connected claw-free graphs',

*Journal of Graph Theory*, vol. 70, no. 1, pp. 40-53. https://doi.org/10.1002/jgt.20599

}

TY - JOUR

T1 - Maximal K 3's and Hamiltonicity of 4-connected claw-free graphs

AU - Fujisawa, Jun

AU - Ota, Katsuhiro

PY - 2012/5

Y1 - 2012/5

N2 - Let cl(G) denote Ryjáček's closure of a claw-free graph G. In this article, we prove the following result. Let G be a 4-connected claw-free graph. Assume that G[N G(T)] is cyclically 3-connected if T is a maximal K 3 in G which is also maximal in cl(G). Then G is hamiltonian. This result is a common generalization of Kaiser et al.'s theorem [J Graph Theory 48(4) (2005), 267-276] and Pfender's theorem [J Graph Theory 49(4) (2005), 262-272].

AB - Let cl(G) denote Ryjáček's closure of a claw-free graph G. In this article, we prove the following result. Let G be a 4-connected claw-free graph. Assume that G[N G(T)] is cyclically 3-connected if T is a maximal K 3 in G which is also maximal in cl(G). Then G is hamiltonian. This result is a common generalization of Kaiser et al.'s theorem [J Graph Theory 48(4) (2005), 267-276] and Pfender's theorem [J Graph Theory 49(4) (2005), 262-272].

KW - claw-free graph

KW - Hamiltonian cycle

KW - maximal K

UR - http://www.scopus.com/inward/record.url?scp=84859889129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859889129&partnerID=8YFLogxK

U2 - 10.1002/jgt.20599

DO - 10.1002/jgt.20599

M3 - Article

AN - SCOPUS:84859889129

VL - 70

SP - 40

EP - 53

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -