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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 24(2) (2004) 249-262
DOI: 10.7151/dmgt.1229


Ken-ichi Kawarabayashi

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



Let G be a graph of order n. Let Kl- 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 Kl-.

This conjecture is motivated by Hajnal and Szemerédi's [6] famous theorem.

In this paper, we verify this conjecture for l=4.

Keywords: extremal graph theory, vertex disjoint copy, minimum degree.

2000 Mathematics Subject Classification: 05C70, 05C38.


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Received 31 August 2002
Revised 6 February 2004