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Discussiones Mathematicae Graph Theory 21(1) (2001) 179-185
DOI: https://doi.org/10.7151/dmgt.1142

VERTEX-DISJOINT STARS IN GRAPHS

Katsuhiro Ota

Department of Mathematics
Keio University
Yokohama, 223-8522 Japan
e-mail: ohta@math.keio.ac.jp

Abstract

In this paper, we give a sufficient condition for a graph to contain vertex-disjoint stars of a given size. It is proved that if the minimum degree of the graph is at least k+t−1 and the order is at least (t+1)k+O(t²), then the graph contains k vertex-disjoint copies of a star K_1,t. The condition on the minimum degree is sharp, and there is an example showing that the term O(t²) for the number of uncovered vertices is necessary in a sense.

Keywords: stars, vertex-disjoint copies, minimum degree.

2000 Mathematics Subject Classification: 05C35, 05C70.

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Received 27 September 2000
Revised 19 March 2001