Induced Decompositions of Highly Dense Graphs

Nathann Cohen (1) , Zsolt Tuza (2, 3)

1 LRI - Laboratoire de Recherche en Informatique
2 MTA SZTAKI - Computer and Automation Research Institute [Budapest]
3 Department of Computer Science and Systems Technology [Veszprem]

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]

Nathann Cohen, Zsolt Tuza. Induced Decompositions of Highly Dense Graphs. Journal of Graph Theory, 2015, 78 (2), pp.97-107. ⟨10.1002/jgt.21792⟩. ⟨hal-01076882⟩