Pawlik, ArkadiuszKozik, JakubKrawczyk, TomaszLason, MichalMicek, PiotrTrotter, William T.Walczak, Bartosz2014-05-262014-05-262014-05-26201410.1016/j.jctb.2013.11.001https://infoscience.epfl.ch/handle/20.500.14299/103681WOS:000334975800002In the 1970s Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer k we construct a triangle-free family of line segments in the plane with chromatic number greater than k. Our construction disproves a conjecture of Scott that graphs excluding induced subdivisions of any fixed graph have chromatic number bounded by a function of their clique number. (C) 2013 Elsevier Inc. All rights reserved.Intersection graphLine segmentsTriangle-freeChromatic numbertext::journal::journal article::research article