On the odd cycle game and connected rules
We study the positional game where two players, Maker and Breaker, alternately select respectively 1 and b previously unclaimed edges of K n . Maker wins if she succeeds in claiming all edges of some odd cycle in K n and Breaker wins otherwise. Improving on a result of Bednarska and Pikhurko, √ we s...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/530634 |
| Acceso en línea: | http://hdl.handle.net/2072/530634 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemàtiques 51 |
| Sumario: | We study the positional game where two players, Maker and Breaker, alternately select respectively 1 and b previously unclaimed edges of K n . Maker wins if she succeeds in claiming all edges of some odd cycle in K n and Breaker wins otherwise. Improving on a result of Bednarska and Pikhurko, √ we show that)(Maker wins the odd cycle game if b ≤ (4 − 6) / 5 + o(1) n. We furthermore introduce ‘‘connected rules’’ and study the oddcycle game under them, both in the Maker–Breaker as well as in the Client–Waiter variant. |
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