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This paper considers a game version of the general position problem in which a general position set is built through adversarial play. Two players in a graph, Builder and Blocker, take it in turns to add a vertex to a set, such that the…

Combinatorics · Mathematics 2024-07-03 Sandi Klavžar , Jing Tian , James Tuite

A polyomino is called a development if it can make a box by folding edges of unit squares forming the polyomino. It is known that there are developments that can fold into a box (or boxes) in multiple ways. In this work, we conducted a…

Discrete Mathematics · Computer Science 2020-05-07 Riona Tadaki , Kazuyuki Amano

We study biased Maker-Breaker games on a graph system $\{G_1,\ldots,G_s\}$, in which Maker's goal is to claim certain rainbow structures, i.e., specified subgraphs consisting of at most one edge from each graph $G_i$. We consider the…

Winning sets of Schmidt's game enjoy a remarkable rigidity. Therefore, this game (and modifications of it) have been applied to many examples of complete metric spaces (X, d) to show that the set of "badly approximable points", with respect…

Dynamical Systems · Mathematics 2013-09-19 Steffen Weil

Kingdomino is a board game designed by Bruno Cathala and edited by Blue Orange since 2016. The goal is to place $2 \times 1$ dominoes on a grid layout, and get a better score than other players. Each $1 \times 1$ domino cell has a color…

Computational Complexity · Computer Science 2020-04-01 Viet-Ha Nguyen , Kevin Perrot , Mathieu Vallet

M\"uller games form a well-established class of games for model checking and verification. These games are played on directed graphs $\mathcal G$ where Player 0 and Player 1 play by generating an infinite path through the graph. The winner…

Computer Science and Game Theory · Computer Science 2023-11-09 Zihui Liang , Bakh Khoussainov , Mingyu Xiao

We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player $A$)…

Dynamical Systems · Mathematics 2015-01-19 Ville Salo , Ilkka Törmä

We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…

Computer Science and Game Theory · Computer Science 2026-05-21 Haris Aziz , Jiarui Gan , Grzegorz Lisowski , Ali Pourmiri

In a $(1:b)$ Maker-Breaker game, a primary question is to find the maximal value of $b$ that allows Maker to win the game (that is, the critical bias $b^*$). Erd\H{o}s conjectured that the critical bias for many Maker-Breaker games played…

Combinatorics · Mathematics 2016-03-15 Michael Krivelevich , Gal Kronenberg

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…

Combinatorics · Mathematics 2019-06-11 Jan Corsten , Adva Mond , Alexey Pokrovskiy , Christoph Spiegel , Tibor Szabó

In set theory without the axiom of regularity, we consider a game in which two players choose in turn an element of a given set, an element of this element, etc.; a player wins if its adversary cannot make any next move. Sets that are…

Logic · Mathematics 2007-05-23 Denis I. Saveliev

By now, the Maker-Breaker connectivity game on a complete graph $K_n$ or on a random graph $G\sim G_{n,p}$ is well studied. Recently, London and Pluh\'ar suggested a variant in which Maker always needs to choose her edges in such a way that…

Combinatorics · Mathematics 2022-08-22 Dennis Clemens , Laurin Kirsch , Yannick Mogge

The Maker-Breaker domination game is a positional game played on a graph by two players called Dominator and Staller. The players alternately select a vertex of the graph that has not yet been chosen. Dominator wins if at some point the…

Combinatorics · Mathematics 2024-06-24 Guillaume Bagan , Eric Duchêne , Valentin Gledel , Tuomo Lehtilä , Aline Parreau

We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vertex is the winner. The game fits into the scheme of several…

Combinatorics · Mathematics 2025-10-31 Sean Fiscus , Glenn Hurlbert , Eric Myzelev , Travis Pence

Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…

Logic in Computer Science · Computer Science 2012-04-04 Krishnendu Chatterjee , Laurent Doyen

Games on recursive game graphs can be used to reason about the control flow of sequential programs with recursion. In games over recursive game graphs, the most natural notion of strategy is the modular strategy, i.e., a strategy that is…

Logic in Computer Science · Computer Science 2014-08-27 Ilaria De Crescenzo , Salvatore La Torre , Yaron Velner

We give an algorithm for solving stochastic parity games with almost-sure winning conditions on {\it lossy channel systems}, under the constraint that both players are restricted to finite-memory strategies. First, we describe a general…

Logic in Computer Science · Computer Science 2019-03-14 Parosh Aziz Abdulla , Lorenzo Clemente , Richard Mayr , Sven Sandberg

A positional game is a game where two players sequentially label vertices of a hypergraph, consisting of a board and a collection of winning sets, with colors assigned to each player until all vertices of the board are claimed. The first…

Combinatorics · Mathematics 2021-09-02 Pranav Avadhanam , Siddhartha G. Jena

We consider concurrent games played by two-players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study a…

Computer Science and Game Theory · Computer Science 2014-09-19 Krishnendu Chatterjee , Rasmus Ibsen-Jensen

This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966),…

Combinatorics · Mathematics 2024-01-17 Urban Larsson , Indrajit Saha , Makoto Yokoo