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Triangle-free planar graphs with the smallest independence number (1606.06265v1)
Published 20 Jun 2016 in math.CO and cs.DM
Abstract: Steinberg and Tovey proved that every n-vertex planar triangle-free graph has an independent set of size at least (n+1)/3, and described an infinite class of tight examples. We show that all n-vertex planar triangle-free graphs except for this one infinite class have independent sets of size at least (n+2)/3.