The Erd{\Ho}s-Faber-Lovász conjecture for geometric graphs

Clemens Huemer, Dolores Lara, Christian Rubio-Montiel

Published 2016-10-05Version 1

We extend the formulation of the original Erd{\H o}s-Faber-Lov{\' a}sz conjecture to complete geometric graphs. We present bounds for the chromatic number of several types of decompositions of the complete geometric graph, in which the vertices are in nonconvex general position. We also consider the case in which the vertices of the complete geometric graph are in convex position, and present bounds for the chromatic number of a few types of decompositions. Finally, we propose a geometric Erd{\H o}s-Faber-Lov{\' a}sz conjecture.