On Grundy indices for complete geometric graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912653867220992 |
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| author | Lara, Dolores Rubio-Montiel, Christian Zaragoza, Francisco |
| author_facet | Lara, Dolores Rubio-Montiel, Christian Zaragoza, Francisco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Grundy indices for complete geometric graphs Lara, Dolores Rubio-Montiel, Christian Zaragoza, Francisco Combinatorics Computational Geometry 05C15, 05C10 G.2.2; G.2.1 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. |
| title | On Grundy indices for complete geometric graphs |
| topic | Combinatorics Computational Geometry 05C15, 05C10 G.2.2; G.2.1 |
| url | https://arxiv.org/abs/2510.15155 |