𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Hamiltonian cycles in 2-connected claw-free-graphs

✍ Scribed by Hao Li

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
418 KB
Volume
20
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

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, where F is the set of all graphs defined as follows: any graph H in F can be decomposed into three vertex disjoint subgraphs H~1~, H~2~, H~3~ such that magnified image, where u~i~, v~i~ ϵ V(H~i~), u~j~ v~j~ ϵ V(H~j~) 1 ϵ i ≦ j ≦ 3. Examples are given to show that the bound n/4 is sharp. © 1995 John Wiley & Sons, Inc.

📜 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 👁 1 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 N2-locally connected claw-fr
Hamiltonian N2-locally connected claw-free graphs
✍ Hong-Jian Lai; Yehong Shao; Mingquan Zhan 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 63 KB

A graph G is N 2 -locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryja ´c ˇek conjectured that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. This conjecture is pro

Claw-free 3-connected P11-free graphs ar
Claw-free 3-connected P11-free graphs are hamiltonian
✍ Tomasz Łuczak; Florian Pfender 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 108 KB 👁 1 views

## 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

Hourglasses and Hamilton cycles in 4-con
Hourglasses and Hamilton cycles in 4-connected claw-free graphs
✍ Tomáš Kaiser; MingChu Li; Zdeněk Ryjáček; Liming Xiong 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 97 KB 👁 1 views

## 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 hamilton