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Coloring intersection graphs of arc-connected sets in the plane (1310.7558v3)
Published 28 Oct 2013 in math.CO, cs.CG, and cs.DM
Abstract: A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line $L$ if the intersection of its any member with $L$ is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.