Factorizations of the complete graphs into factor of subdiameter two and factors of diameter three

摘要

We search for the minimal number of vertices of the complete graph that can be decomposed into one factor of subdiameter 2 and k factors of diameter 3. We find as follows: exact values for k≤3, upper and lower bounds for small values of k and [lim_{krightarrow infty }frac{phi left( kright) }{k}=2.]