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On the odd cycle game and connected rules

Corsten, J; Mond, A; Pokrovskiy, A; Spiegel, C; Szabo, T; (2020) On the odd cycle game and connected rules. European Journal of Combinatorics , 89 , Article 103140. 10.1016/j.ejc.2020.103140.

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Abstract

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.

Type: Article
Title: On the odd cycle game and connected rules
DOI: 10.1016/j.ejc.2020.103140
Publisher version: https://doi.org/10.1016/j.ejc.2020.103140
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10112637
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