| Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2929 - 2939 | |
| DOI | https://doi.org/10.1051/ro/2023162 | |
| Published online | 13 November 2023 | |
Bichromatic coloring game on triangulations
Research Institute for Digital Media and Content, Keio University, Hiyoshi Campus West Annex 1, 2-1-1 Hiyoshihoncho, Kouhoku-ku, Yokohama, Kanagawa 223-8523, Japan
* Corresponding author: naoki.matsumo10@gmail.com
Received:
6
December
2022
Accepted:
3
October
2023
In this paper, we study bichromatic coloring game on a disk triangulation, which is introduced by Aichholzer et al. in 2005. They proved that if a disk triangulation has at most two inner vertices, then the second player can force a tie in the bichromatic coloring game on the disk triangulation. We prove that the same statement holds for any disk triangulation with at most four inner vertices, and that the bound of the number of inner vertices is the best possible. Furthermore, we consider the game on topological triangulations.
Mathematics Subject Classification: 05C57 / 05C10 / 91A43
Key words: Bichromatic coloring game / triangulation / combinatorial game
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
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