Issue |
RAIRO-Oper. Res.
Volume 58, Number 2, March-April 2024
|
|
---|---|---|
Page(s) | 1759 - 1770 | |
DOI | https://doi.org/10.1051/ro/2024054 | |
Published online | 16 April 2024 |
The (a, b)-monochromatic transversal game on clique-hypergraphs of powers of cycles *, **
1
DEX, Universidade do Estado de Minas Gerais, Belo Horizonte, Brazil
2
IME, Universidade Federal Fluminense, Niterói, Brazil
3
CNRS, Université Grenoble Alpes, Saint-Martin-d’Hères, France
* Corresponding author: sdantas@id.uff.br
Received:
11
November
2022
Accepted:
4
March
2024
We study the (a, b)-monochromatic transversal game that is a combinatorial Maker–Breaker game where Alice and Bob alternately colour a vertices in red and b vertices in blue of a hypergraph, respectively. Either player is enabled to start the game. Alice tries to construct a hyperedge transversal, and Bob tries to prevent this. The winner is Alice if she obtains a red hyperedge transversal; otherwise, Bob wins the game if he obtains a monochromatic blue hyperedge. Maker–Breaker games were determined to be PSPACE-complete. In this work, we analyze the game played on clique-hypergraphs of powers of cycles, and we show strategies that, depending on the choice of the parameters, allow a specific player to win the game.
Mathematics Subject Classification: 05C57 / 05C15 / 05C65
Key words: Combinatorial games / hypergraphs / transversal
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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