Geometric achromatic and pseudoachromatic indices
Oswin Aichholzer, Gabriela Araujo‐Pardo, Thomas Hackl, Dolores Lara, Christian Rubio-Montiel, J. Urrutia, et al. · 2015
The pseudoachromatic index of a graph is the maximum number of col-ors that can be assigned to its edges, such that each pair of different colors is incident to a common vertex. If for each vertex its incident edges have different color, then this maximum is known as achromatic index. Both indices have been widely studied. A geometric graph is a graph drawn in the plane such that its vertices are points in general position, and its edges are straight-line segments. In this paper we extend the notion of pseu-doachromatic and achromatic indices for geometric graphs, and present results for complete geometric graphs. In particular, we show that for n points in convex position the achromatic index and the pseudoachromatic index of the complete geometric graph are bn2+n 4 c.