Abstract
Gyarfas conjectured that in every r -edge-coloring of the complete graph K n there is a monochromatic component on at least n ∕ ( r − 1 ) vertices which has diameter at most 3. We show that for r = 3 , 4 , 5 and 6 a diameter of 3 is best possible in this conjecture, constructing colorings where every monochromatic diameter-2 subgraph has strictly less than n ∕ ( r − 1 ) vertices.
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