#### 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 *K*_{n} 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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