𝔖 Bobbio Scriptorium
✦   LIBER   ✦

9-Connected Claw-Free Graphs Are Hamilton-Connected

✍ Scribed by Stephan Brandt

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
130 KB
Volume
75
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.

✦ Synopsis

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 line graphs.

📜 SIMILAR VOLUMES

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

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 👁 2 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 👁 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

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 👁 1 views

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