On the odd cycle game and connected rules
Corsten, J., Mond, A., Pokrovskiy, A., Spiegel, C. & Szabó, T.
(2020).
On the odd cycle game and connected rules.
European Journal of Combinatorics,
89,
https://doi.org/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.
