The Erd{\Ho}s-Faber-Lov\'asz conjecture for geometric graphs
Clemens Huemer, Dolores Lara, Christian Rubio-Montiel · arXiv (Cornell University) · 2016
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.