Vertex-disjoint copies of K¯₄

Ken-ichi Kawarabayashi

ArticleOriginal scientific text

Title

Vertex-disjoint copies of K¯₄

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Affiliations

Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

Abstract

Let G be a graph of order n. Let K¯ₗ be the graph obtained from Kₗ by removing one edge. In this paper, we propose the following conjecture: Let G be a graph of order n ≥ lk with δ(G) ≥ (n-k+1)(l-3)/(l-2)+k-1. Then G has k vertex-disjoint K¯ₗ. This conjecture is motivated by Hajnal and Szemerédi's [6] famous theorem. In this paper, we verify this conjecture for l=4.

Keywords

ENG

extremal graph theory, vertex disjoint copy, minimum degree

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Title

Vertex-disjoint copies of K¯₄

Affiliations

Abstract

Keywords

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