𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Circumference of 3-Connected Quasi-Claw-Free Graphs

✍ Scribed by Elkin Vumar

Publisher
Springer Japan
Year
2006
Tongue
English
Weight
152 KB
Volume
22
Category
Article
ISSN
0911-0119

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Critical graphs for subpancyclicity of 3
Critical graphs for subpancyclicity of 3-connected claw-free graphs
✍ Ronald J. Gould; Tomasz Łuczak; Florian Pfender 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 173 KB

## Abstract Let ${\cal{F}}\_{k}$ be the family of graphs __G__ such that all sufficiently large __k__ ‐connected claw‐free graphs which contain no induced copies of __G__ are subpancyclic. We show that for every __k__≥3 the family ${\cal{F}}\_{1}k$ is infinite and make the first step toward the c

On factors of 4-connected claw-free grap
On factors of 4-connected claw-free graphs
✍ H. J. Broersma; M. Kriesell; Z. Ryjác̆ek 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 105 KB

## Abstract We consider the existence of several different kinds of factors in 4‐connected claw‐free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4‐connected line graph is hamiltonian,

Degree bounds for the circumference of 3
Degree bounds for the circumference of 3-connected graphs
✍ Heinz A. Jung; Elkin Vumar 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 229 KB 👁 1 views

## Abstract Let __C__ be a longest cycle in the 3‐connected graph __G__ and let __H__ be a component of __G__ − __V__(__C__) such that |__V__(__H__)| ≥ 3. We supply estimates of the form |__C__| ≥ 2__d__(__u__) + 2__d__(__v__) − α(4 ≤ α ≤ 8), where __u__,__v__ are suitably chosen non‐adjacent verti

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

On the Circumferences of Regular 2-Conne
On the Circumferences of Regular 2-Connected Graphs
✍ Bing Wei 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 135 KB

Let G be a 2-connected d-regular graph on n rd (r 3) vertices and c(G) denote the circumference of G. Bondy conjectured that c(G) 2nÂ(r&1) if n is large enough. In this paper, we show that c(G) 2nÂ(r&1)+2(r&3)Â(r&1) for any integer r 3. In particular, G is hamiltonian if r=3. This generalizes a resu