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arXiv · 1303.4673

Geometric achromatic and pseudoachromatic indices

O. Aichholzer·G. Araujo-Pardo·N. García-Colín·T. Hackl·D. Lara·C. Rubio-Montiel·J. Urrutia
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Abstract

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 $\lfloor \tfrac{n^2+n}{4} \rfloor$.

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O. Aichholzer, G. Araujo-Pardo, N. García-Colín, T. Hackl, D. Lara, C. Rubio-Montiel, J. Urrutia. 2013-03-19. Geometric achromatic and pseudoachromatic indices. https://doi.org/10.1007/s00373-015-1610-x

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