Bounds on the chromatic number of intersection graphs of sets in the plane

I.G. Perepelitsa
2003 Discrete Mathematics  
In this paper we show that the chromatic number of intersection graphs of congruent geometric ÿgures obtained by translations of a ÿxed ÿgure in the plane is bounded by the clique number. Further, in the paper we prove that the triangle-free intersection graph of a ÿnite number of compact connected sets with piecewise di erentiable Jordan curve boundaries is planar and hence, is 3-colorable.
doi:10.1016/s0012-365x(02)00501-0 fatcat:46e5neusdrabvdbqmwescupt6a