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arXiv · 2510.15155

On Grundy indices for complete geometric graphs

Dolores Lara·Christian Rubio-Montiel·Francisco Zaragoza
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Abstract

The pseudo-Grundy index of a graph is the largest number of colors that can be assigned to its edges, such that for every pair of colors $i,j$, if $i < j$ then every edge colored with color $j$ is adjacent to at least one edge colored with color $i$. This index has 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 pseudo-Grundy index for geometric graphs, and present results for complete geometric graphs.

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Dolores Lara, Christian Rubio-Montiel, Francisco Zaragoza. 2025-10-16. On Grundy indices for complete geometric graphs. https://arxiv.org/abs/2510.15155

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