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Local Shearer Bound for Fractional Coloring of Triangle-Free Graphs

A local strengthening of Shearer's bound guaranteeing, for every triangle-free graph, a probability distribution over independent sets in which each vertex v appears with probability at least (1-o(1))*ln(d(v))/d(v). It resolves the Kelly-Postle local fractional coloring conjecture and yields upper bounds on the fractional chromatic number of triangle-free graphs in terms of vertex count, edge count, and spectral radius.