𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Hamilton connectivity of line graphs and claw-free graphs

✍ Scribed by Zhiquan Hu; Feng Tian; Bing Wei

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
117 KB
Volume
50
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

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‐connected claw‐free graph is Hamilton‐connected. Several related results known before are generalized. © 2005 Wiley Periodicals, Inc. J Graph Theory

📜 SIMILAR VOLUMES

9-Connected Claw-Free Graphs Are Hamilto
9-Connected Claw-Free Graphs Are Hamilton-Connected
✍ Stephan Brandt 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 130 KB

A graph is Hamilton-connected if any pair of vertices is joined by a hamiltonian path. In this note it is shown that 9-connected graphs which contain no induced claw K 1, 3 are Hamilton-connected, by reformulating and localizing a closure concept due to Ryja c ek, which turns claw-free graphs into l

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 👁 2 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

Hamiltonicity and Minimum Degree in 3-co
Hamiltonicity and Minimum Degree in 3-connected Claw-Free Graphs
✍ Odile Favaron; Pierre Fraisse 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 112 KB

Using Ryja c ek's closure, we prove that any 3-connected claw-free graph of order & and minimum degree $ &+38 10 is hamiltonian. This improves a theorem of Kuipers and Veldman who got the same result with the stronger hypotheses $ &+29 8 and & sufficiently large and nearly proves their conjecture sa

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