Induced Decompositions of Highly Dense Graphs
Résumé
Given two graphs F and G, an induced F -decomposition of G is a partition of E(G) into induced subgraphs isomorphic to F . Bondy and Szwarc-fiter [J. Graph Theory, DOI: 10.1002/jgt.21654] defined the value ex*(n, F) as the maximum number of edges in a graph of order n admitting an induced F -decomposition and determined the value of ex * (n, F) for some graphs (and families of graphs). In this paper we prove that ex * (n, F) = n 2 −o(n 2) is valid for all graphs F . We also present tighter asymptotic bounds for some of the small graphs for which the exact value of ex * remains unknown. The proofs are based on the heavy use of various classes of Kneser graphs and hypergraphs.
Domaines
Combinatoire [math.CO]Origine | Fichiers produits par l'(les) auteur(s) |
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