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On the odd cycle game and connected rules

Corsten, Jan, Mond, Adva, Pokrovskiy, Alexey, Spiegel, Christoph and Szabó, Tibor (2020) On the odd cycle game and connected rules. European Journal of Combinatorics, 89. ISSN 0195-6698

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Identification Number: 10.1016/j.ejc.2020.103140


We study the positional game where two players, Maker and Breaker, alternately select respectively 1 and b previously unclaimed edges of Kn. Maker wins if she succeeds in claiming all edges of some odd cycle in Kn 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 odd cycle game under them, both in the Maker–Breaker as well as in the Client–Waiter variant.

Item Type: Article
Official URL:
Additional Information: © 2020 Elsevier Ltd
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 08 Jul 2020 09:57
Last Modified: 20 Oct 2021 02:51

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