Trivial colors in colorings of Kneser graphs
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We show that any proper coloring of a Kneser graph KG_n,k with n-2k+2 colors contains a trivial color (i.e., a color consisting of sets that all contain a fixed element), provided n>(2+ϵ)k^2, where ϵ→ 0 as k→∞. This bound is essentially tight.
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