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Discussiones Mathematicae Graph Theory 23(1) (2003) 37-54
DOI: https://doi.org/10.7151/dmgt.1184

DECOMPOSITION OF COMPLETE GRAPHS INTO FACTORS OF DIAMETER TWO AND THREE

Damir Vukicević

Department of Mathematics
University of Split
Teslina 12, 21000 Split, Croatia

Abstract

We analyze a minimum number of vertices of a complete graph that can be decomposed into one factor of diameter 2 and k factors of diameter at most 3. We find exact values for k ≤ 4 and the asymptotic value of the ratio of this number and k when k tends to infinity. We also find the asymptotic value of the ratio of the number of vertices of the smallest complete graph that can be decomposed into p factors of diameter 2 and k factors of diameter 3 and number k when p is fixed.

Keywords: decomposition, graph.

2000 Mathematics Subject Classification: 05C70.

References

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Received 25 May 2001
Revised 5 September 2002