𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Hourglasses and Hamilton cycles in 4-connected claw-free graphs

✍ Scribed by Tomáš Kaiser; MingChu Li; Zdeněk Ryjáček; Liming Xiong

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
97 KB
Volume
48
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 267–276, 2005

📜 SIMILAR VOLUMES

Hamiltonian cycles in 3-connected claw-f
Hamiltonian cycles in 3-connected claw-free graphs
✍ MingChu Li 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 437 KB 👁 2 views

## Abstract In this paper, we show that every 3‐connected claw‐free graph on n vertices with δ ≥ (__n__ + 5)/5 is hamiltonian. © 1993 John Wiley & Sons, Inc.

Hamiltonian cycles in 2-connected claw-f
Hamiltonian cycles in 2-connected claw-free-graphs
✍ Hao Li 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 418 KB 👁 2 views

## Abstract M. Matthews and D. Sumner have proved that of __G__ is a 2‐connected claw‐free graph of order __n__ such that δ ≧ (__n__ − 2)/3, then __G__ is hamiltonian. We prove that the bound for the minimum degree δ can be reduced to __n__/4 under the additional condition that __G__ is not in __F_

Hamilton connectivity of line graphs and
Hamilton connectivity of line graphs and claw-free graphs
✍ Zhiquan Hu; Feng Tian; Bing Wei 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 117 KB

## Abstract Let __G__ be a graph and let __V__~0~ = {ν∈ __V__(__G__): __d__~__G__~(ν) = 6}. We show in this paper that: (i) if __G__ is a 6‐connected line graph and if |__V__~0~| ≤ 29 or __G__[__V__~0~] contains at most 5 vertex disjoint __K__~4~'s, then __G__ is Hamilton‐connected; (ii) every 8‐co

Maximal K3's and Hamiltonicity of 4-conn
Maximal K3's and Hamiltonicity of 4-connected claw-free graphs
✍ Jun Fujisawa; Katsuhiro Ota 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 255 KB 👁 1 views

## 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 maxim