Glasnik Matematicki, Vol. 38, No.2 (2003), 211-232.

MIX-DECOMPOSITION OF THE COMPLETE GRAPH INTO DIRECTED FACTORS OF DIAMETER 2 AND UNDIRECTED FACTORS OF DIAMETER 3

Damir Vukičević

Department of Mathematics, University of Split, Teslina 12, 21000 Split, Croatia
e-mail: damir.vukicevic@pmfst.hr


Abstract.   We estimate the values, for each k, of the smallest n such that Kn can be mix-decomposed into k undirected factors of diameter 3 and one directed factor of diameter 2. We find the asymptotic value of ratio of n and k, when k tends to infinity and generalize this result for mix-decompositions into p directed factors of diameter 2 and k undirected factors of diameter 3.

2000 Mathematics Subject Classification.   05C70.

Key words and phrases.   Decomposition, mix-decomposition, factor, graph.


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