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Closure concepts for claw-free graphs

✍ Scribed by H.J. Broersma; H. Trommel


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
404 KB
Volume
185
Category
Article
ISSN
0012-365X

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On a Closure Concept in Claw-Free Graphs
✍ Zdeněk Ryjáček 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 269 KB

If G is a claw-free graph, then there is a graph cl(G) such that (i) G is a spanning subgraph of cl(G), (ii) cl(G) is a line graph of a triangle-free graph, and (iii) the length of a longest cycle in G and in cl(G) is the same. A sufficient condition for hamiltonicity in claw-free graphs, the equiv

Closure and stable Hamiltonian propertie
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In the class of k-connected claw-free graphs, we study the stability of some Hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these

Closure, 2-factors, and cycle coverings
✍ Ryj�?ek, Zden?k; Saito, Akira; Schelp, R. H. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 239 KB 👁 3 views

In this article, we study cycle coverings and 2-factors of a claw-free graph and those of its closure, which has been defined by the first author (On a closure concept in claw-free graphs, J Combin Theory Ser B 70 (1997), 217-224). For a claw-free graph G and its closure cl(G), we prove: ( 1 (2) G

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

Quasi-claw-free graphs
✍ A. Ainouche 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 645 KB

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.

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