Georgia Institute of Technology College of Sciences

Grötzsch's theorem implies that every planar triangle-free graph is 3-colorable. It is natural to ask whether this can be improved. We prove that every planar triangle-free graph on n vertices has fractional chromatic number at most 3-1/(n+1/3), while Jones constructed planar triangle-free n-vertex graphs with fractional chromatic number 3-3/(n+1). We also investigate additional conditions under that triangle-free planar graphs have fractional chromatic number smaller than 3-epsilon for some fixed epsilon > 0.(joint work with J.-S. Sereni and J. Volec)