Geometric achromatic and pseudoachromatic indices

Oswin Aichholzer, G. Araujo-Pardo, N. García-Colín, Thomas Hackl, N. Lara, C. Rubio-Montinel, J. Urrutia

Research output: Contribution to journalArticlepeer-review


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 (Formula presented.).
Original languageEnglish
Pages (from-to)431-451
JournalGraphs and Combinatorics
Issue number2
Publication statusPublished - 2016

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