Geometric Achromatic and Pseudoachromatic Indices

The pseudoachromatic index of a graph is the maximum number of colors 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 pseudoachromatic 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 n2 +n 4 .

• Type: Journal
• Year: 2016
• Where: GC
• Authors: Oswin Aichholzer, Gabriela Araujo-Pardo, Natalia García-Colín, Thomas Hackl, Dolores Lara, C. Rubio-Montiel, Jorge Urrutia
• Keywords: Applied Computing, GC 2016