2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79036Given a coloring of the edges of the complete graph on n vertices in k colors, by considering the neighbors of an arbitrary vertex it follows that there is a monochromatic diameter two subgraph on at least 1+(n-1)/k vertices. We show that for $k \ge 3$ this is asymptotically best possible, and that for k=2 there is always a monochromatic diameter two subgraph on at least $\lceil {3 \over 4} n \rceil$ vertices, which again, is best possible.20 pagesCombinatoricstext