✦ LIBER ✦

Quasi-claw-free graphs

✍ Scribed by A. Ainouche

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 645 KB
Volume: 179
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00023-x

No coin nor oath required. For personal study only.

✦ Synopsis

A graph G is quasi claw-free if it satisfies the property:

This property is satisfied if in particular u does not center a claw (induced K1.3). Many known results on claw-free graphs, dealing with matching and hamiltonicity are extended to the larger class of quasi-claw-free graphs.

📜 SIMILAR VOLUMES

Almost claw-free graphs

✍ Zdeněk Ryjáček 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 374 KB

## Abstract We say that __G__ is almost claw‐free if the vertices that are centers of induced claws (__K__~1,3~) in __G__ are independent and their neighborhoods are 2‐dominated. Clearly, every claw‐free graph is almost claw‐free. It is shown that (i) every even connected almost claw‐free graph has

Claw-free circular-perfect graphs

✍ Arnaud Pêcher; Xuding Zhu 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 112 KB

## Abstract The circular chromatic number of a graph is a well‐studied refinement of the chromatic number. Circular‐perfect graphs form a superclass of perfect graphs defined by means of this more general coloring concept. This article studies claw‐free circular‐perfect graphs. First, we prove that

Well-Covered Claw-Free Graphs

✍ David Tankus; Michael Tarsi 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 336 KB

On hamiltonian claw-free graphs

✍ E. Flandrin; J.L. Fouquet; H. Li 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 515 KB

We show that every 3-connected claw-free graphs having at most 5S-10 vertices is hamiltonian, where 6 is the minimum degree. For regular 3-connected claw-free graphs, a related result was obtained by Li and Liu (preprint), but for nonregular claw-free graphs the best-known result comes from the work

Triangles in claw-free graphs

✍ Hong Wang 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 642 KB

A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to KI,3. Let k be a positive integer. Our main result is as follows: If G is a claw-free graph of order at least 3k and d(x) + d(y)>~3k + 1 for every pair of non-adjacent vertices x and y of G, then G contains k v

Hamilton cycles in claw-free graphs

✍ Cun-Quan Zhang 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 299 KB 👁 2 views