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Packing and covering dense graphs

โœ Scribed by Noga Alon; Yair Caro; Raphael Yuster


Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
498 KB
Volume
6
Category
Article
ISSN
1063-8539

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A graph is well-covered if every maximal independent set is maximum. This concept, introduced by Plummer in 1970 (J. Combin. Theory 8 (1970)), is the focal point of much interest and current research. We consider well-covered 2-degenerate graphs and supply a structural (and polynomial time algorithm

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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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For a graph G, let ฯƒ 3 (G) = min{deg G x + deg G y + deg G z: {x, y, z} is an independent set in G}. Enomoto et al. [Enowoto et al., J Graph Theory 20 (1995), 419-422] have proved that the vertex set of a 2-connected graph G of order n with ฯƒ 3 (G) โ‰ฅ n is covered by two cycles, edges or vertices. Ex