Induced Complete h-partite Graphs in Dense Clique-less Graphs

It is proven that for every fixed h, a and b, a graph with n vertices and minimum degree at least h-1 h n, which contains no copy of Kb (the complete graph with b vertices), contains at least (1 - o(1)) n ha vertex disjoint induced copies of the complete h-partite graph with a vertices in each color class. Mathematics subject classification numbers: 05C70, 05C55. All graphs considered here are finite, undirected, and have neither loops nor parallel edges. The notation here follows the convention of [4] except where stated otherwise. Many asymptotic embedding results have been proven by the Regularity Lemma of Szemer

• Type: Journal
• Year: 1999
• Where: COMBINATORICS
• Authors: Eldar Fischer
• Keywords: COMBINATORICS 1999, Complete H-partite Graph, Ha Vertex, Minimum Degree