Arkadiusz Pawlik

TL;DR: In this article, it was shown that the chromatic number of intersection graphs of line segments in the plane is not bounded by a function of their clique number, which disproved a conjecture of Scott that graphs excluding induced subdivisions of any fixed graph have chromatic numbers bounded by their cliques number.

TL;DR: The construction of a triangle-free family of line segments in the plane with chromatic number greater than $k$ 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.

TL;DR: In this paper, a general construction for intersection graphs of geometric objects in the plane is presented, where the chromatic number of a graph may be arbitrarily large compared to its clique number.

TL;DR: A general construction that for any arc-connected compact set X in R2 that is not an axis-aligned rectangle and for any positive integer k produces a family F of sets, each obtained by an independent horizontal and vertical scaling and translation of X, provides a negative answer to a question of Gyárfás and Lehel for L-shapes.

TL;DR: 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.