Disjoint Color-Avoiding Triangles

A set of pairwise edge-disjoint triangles of an edge-colored Kn is r-color avoiding if it does not contain r monochromatic triangles, each having a different color. Let fr(n) be the maximum integer so that in every edge coloring of Kn with r colors, there is a set of fr(n) pairwise edge-disjoint triangles that is r-color avoiding. We prove that 0.1177n2(1 - o(1)) < f2(n) < 0.1424n2(1 + o(1)). The proof of the lower bound uses probabilistic arguments, fractional relaxation and some packing theorems. We also prove that fr(n)/n2 < 1 6 (1 - 0.145r-1) + o(1). In particular, for every r, if n is sufficiently large, there are edge colorings of Kn with r colors so that the removal of any o(n2) members from any Steiner triple system does not turn it r-color avoiding. Key words. edge coloring, packing, triangles AMS subject classifications. 05C15, 05C35, 05C70

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: Raphael Yuster
• Keywords: Edge-colored Kn, Edge-disjoint Triangles, Monochromatic Triangles, SIAMDM 2008