### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 95-109 |

Number of pages | 15 |

Journal | Ars combinatoria |

Volume | 124 |

Publication status | Published - Jan 2016 |

### Keywords

- EWI-27151
- MSC-05C
- IR-101070
- METIS-318496
- Hamilton-connected
- Hamiltonian
- almost locally connected
- Claw-free graph

### Cite this

*Ars combinatoria*,

*124*, 95-109.

}

*Ars combinatoria*, vol. 124, pp. 95-109.

**Hamiltonian properties of almost locally connected claw-free graphs.** / Chen, Xiaodong; Li, MingChu; Liao, Wei; Broersma, Haitze J.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Hamiltonian properties of almost locally connected claw-free graphs

AU - Chen, Xiaodong

AU - Li, MingChu

AU - Liao, Wei

AU - Broersma, Haitze J.

N1 - eemcs-eprint-27151

PY - 2016/1

Y1 - 2016/1

N2 - A vertex v of a graph G is locally connected if the set of neighbors N(v) of v induces a connected subgraph in G. Let B(G) denote the set of vertices of G that are not locally connected. Then G is almost locally connected if B(G) is an independent set and for any vertex x in B(G), there is a vertex y in V(G) - x such that N(x) ∪ y induces a connected subgraph of G. The main result of this paper is that an almost locally connected claw-free graph on at least 4 vertices is Hamilton-connected if and only if it is 3-connected. This generalizes the result by Asratian that a locally connected claw-free graph on at least 4 vertices is Hamilton-connected if and only if it is 3-connected [Journal of Graph Theory 23 (1996) 191–201].

AB - A vertex v of a graph G is locally connected if the set of neighbors N(v) of v induces a connected subgraph in G. Let B(G) denote the set of vertices of G that are not locally connected. Then G is almost locally connected if B(G) is an independent set and for any vertex x in B(G), there is a vertex y in V(G) - x such that N(x) ∪ y induces a connected subgraph of G. The main result of this paper is that an almost locally connected claw-free graph on at least 4 vertices is Hamilton-connected if and only if it is 3-connected. This generalizes the result by Asratian that a locally connected claw-free graph on at least 4 vertices is Hamilton-connected if and only if it is 3-connected [Journal of Graph Theory 23 (1996) 191–201].

KW - EWI-27151

KW - MSC-05C

KW - IR-101070

KW - METIS-318496

KW - Hamilton-connected

KW - Hamiltonian

KW - almost locally connected

KW - Claw-free graph

M3 - Article

VL - 124

SP - 95

EP - 109

JO - Ars combinatoria

JF - Ars combinatoria

SN - 0381-7032

ER -