Bounds on the chromatic number of intersection graphs of sets in the plane Original Research Article

In this paper we show that the chromatic number of intersection graphs of congruent geometric figures obtained by translations of a fixed figure in the plane is bounded by the clique number. Further, in the paper we prove that the triangle-free intersection graph of a finite number of compact connected sets with piecewise differentiable Jordan curve boundaries is planar and hence, is 3-colorable.