On a Certain Type of Decompositions of Complete Graphs into Factors with Equal Diameters

Daniel Palumbíny

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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. ...