1
2003.
Decomposition of complete graphs into factors of diameter two and three
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.