Sparse Graphs Coalition

We play positional games on edge sets of graphs, two players alternately claim unclaimed edges of a given graph until all the edges are claimed. There are several variants of positional games:

• In a Maker-Breaker game Maker wants to achieve a graph property (fixed in advance, say “having a triangle”) on the graph she claimed. Breaker wants to prevent her from doing that.
• In an Avoider-Enforcer game, Enforcer wins if Avoider has the property on her graph, and Avoider wins otherwise.
• Etc.

Generally, given a game (i.e. given a base graph, a target graph property, and a variant of positional game) we want to figure out which player has a winning strategy. (It is known that one player must have a winning strategy.)

• If the game is played on a random graph, we study the probability for a player to win.
• Given a graph property, we may ask what's the smallest graph density on which a player can win.
• Etc.

We can choose a more focused topic, depending on the interest. In any case, there is a number of open problems to work on.

Mirjana Mikalački and Miloš Stojaković

13-17 September 2021

• Mirjana Mikalački (organiser), University of Novi Sad
• Miloš Stojaković (organiser), University of Novi Sad
• Grzegorz Adamski, Adam Mickiewicz University Poznan
• Małgorzata Bednarska-Bzdęga, Adam Mickiewicz University Poznan
• Dennis Clemens, TU Hamburg
• Vojtech Dvorak, University of Cambridge, UK
• Asaf Ferber, University of California Irvine
• Jovana Forcan, University of Novi Sad
• Pranshu Gupta, TU Hamburg
• Fabian Hamann, TU Hamburg
• Michael Krivelevich, Tel Aviv University
• Ander Lamaison, Masaryk University in Brno
• Thomas Lesgourges, UNSW Sydney
• Anita Liebenau, UNSW Sydney
• Allan Lo, University of Birmingham, UK
• Tomasz Łuczak, Adam Mickiewicz University Poznan
• Yannick Mogge, TU Hamburg
• Tobias Müller, Groningen University
• Nacim Oijid, LIRIS, Université Lyon 1
• Amedeo Sgueglia, London School of Economics
• Jelena Stratijev, University of Novi Sad
• Tuan Tran, IBS Daejeon Korea
• Marcin Witkowski, Adam Mickiewicz University Poznan

Registration details: closed August 29th.

Submission details: Send them by email to the organizers.

Submission deadline: Friday September 10th, 2021 (AoE)

1. Monday
  * 10:00 (CET) Miloš Stojaković: Tutorial on Positional Games 
    (The tutorial is meant for those who would like to brush up their knowledge on positional games.)
  * 14:00 (CET) Open Problem Session
2. Tuesday - Friday
  * Work in groups.

Zoom link to tutorial: https://us02web.zoom.us/j/85951587794?pwd=WkxQekluNHBmOHlSSllxSVhaRHR2dz09

• Barkey, Clemens, Hamann, Mikalački, Sgueglia. Multistage positional games. https://arxiv.org/abs/2202.04344