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Closure and stable Hamiltonian properties in claw-free graphs

✍ Scribed by Brandt, Stephan; Favaron, Odile; Ryj�?ek, Zden?k

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
171 KB
Volume
34
Category
Article
ISSN
0364-9024

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✦ Synopsis

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 properties there is an infinite family of graphs G k of arbitrarily high connectivity k such that the closure of G k has the property while the graph G k does not); (ii) traceability is a stable property even for k = 1; (iii) homogeneous traceability is not stable for k = 2 (although it is stable for k = 7).

📜 SIMILAR VOLUMES

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

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Toughness and hamiltonicity in almost claw-free graphs
✍ Broersma, H.J.; Ryj�?ek, Z.; Schiermeyer, I. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 491 KB 👁 1 views

Some known results on claw-free (Kl,3-free) graphs are generalized to the larger class of almost claw-free graphs which were introduced by RyjaEek. In particular, w e show that a 2-connected almost claw-free graph is I-tough, and that a 2-connected almost claw-free graph on n vertices is hamiltonian