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This paper considers a game in which a single cop and a single robber take turns moving along the edges of a given graph $G$. If there exists a strategy for the cop which enables it to be positioned at the same vertex as the robber…

Data Structures and Algorithms · Computer Science 2019-08-20 Thomas Erlebach , Jakob T. Spooner

Let $p,q$ be two integers with $p\geq q$. Given a finite graph $F$ with no isolated vertices, the generalized Ramsey achievement game of $F$ on the complete graph $K_n$, denoted by $(p,q;K_n,F,+)$, is played by two players called Alice and…

Combinatorics · Mathematics 2024-08-06 Zhong Huang , Yusuke Kobayashi , Yaping Mao , Bo Ning , Xiumin Wang

The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$. The goal of Dominator is to form a dominating set with the set of vertices…

Combinatorics · Mathematics 2025-12-10 Athira Divakaran , Tanja Dravec , Tijo James , Sandi Klavžar , Latha S Nair

We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this paper we consider the scenario when Maker plays randomly and Breaker is "clever", and…

Combinatorics · Mathematics 2016-04-01 Jonas Groschwitz , Tibor Szabó

In the graph avoidance game two players alternatingly color edges of a graph G in red and in blue respectively. The player who first creates a monochromatic subgraph isomorphic to a forbidden graph F loses. A symmetric strategy of the…

Discrete Mathematics · Computer Science 2007-05-23 Frank Harary , Wolfgang Slany , Oleg Verbitsky

We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the…

Formal Languages and Automata Theory · Computer Science 2020-02-19 Dhananjay Raju , Rüdiger Ehlers , Ufuk Topcu

We investigate Maker-Breaker games on graphs of size $\aleph_1$ in which Maker's goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the game on the axiomatic framework. Relating to this, we prove…

Combinatorics · Mathematics 2023-06-16 Nathan Bowler , Florian Gut , Attila Joó , Max Pitz

We consider a biased version of Maker-Breaker domination games, which were recently introduced by Gledel, Ir{\v{s}}i{\v{c}}, and Klav{\v{z}}ar. Two players, Dominator and Staller, alternatingly claim vertices of a graph $G$ where Dominator…

Combinatorics · Mathematics 2024-08-02 Ali Deniz Bagdas , Dennis Clemens , Fabian Hamann , Yannick Mogge

We look at the unbiased Maker-Breaker Hamiltonicity game played on the edge set of a complete graph $K_n$, where Maker's goal is to claim a Hamiltonian cycle. First, we prove that, independent of who starts, Maker can win the game for $n =…

Combinatorics · Mathematics 2018-08-08 Miloš Stojaković , Nikola Trkulja

We study (a:a) Maker-Breaker games played on the edge set of the complete graph on n vertices. In the following four games - perfect matching game, Hamilton cycle game, star factor game and path factor game, our goal is to determine the…

Combinatorics · Mathematics 2016-02-09 Dennis Clemens , Mirjana Mikalački

We study two-player multi-weighted reachability games played on a finite directed graph, where an agent, called P1, has several quantitative reachability objectives that he wants to optimize against an antagonistic environment, called P2.…

Computer Science and Game Theory · Computer Science 2025-09-08 Thomas Brihaye , Aline Goeminne

Concurrent parameterized games involve a fixed yet arbitrary number of players. They are described by finite arenas in which the edges are labeled with languages that describe the possible move combinations leading from one vertex to…

Logic in Computer Science · Computer Science 2025-05-22 Nathalie Bertrand , Patricia Bouyer , Gaëtan Staquet

We introduce a general framework for positional games in which players score points by claiming a prescribed portion of each winning set, extending the notion of scoring Maker-Breaker games. In the scoring variant, Maker gains a point by…

Discrete Mathematics · Computer Science 2026-03-06 Eric Duchêne , Valentin Gledel , Miloš Stojaković

We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a…

Combinatorics · Mathematics 2024-02-12 Dana C. Ernst , Nandor Sieben

We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…

We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has the complete information. We look at the biased $(a:b)$…

Combinatorics · Mathematics 2025-07-31 Dennis Clemens , Fabian Hamann , Mirjana Mikalački , Yannick Mogge , Miloš Stojaković

We study Maker/Breaker games on the edges of sparse graphs. Maker and Breaker take turns in claiming previously unclaimed edges of a given graph H. Maker aims to occupy a given target graph G and Breaker tries to prevent Maker from…

Combinatorics · Mathematics 2011-06-17 Heidi Gebauer

Regular games form a well-established class of games for analysis and synthesis of reactive systems. They include coloured Muller games, McNaughton games, Muller games, Rabin games, and Streett games. These games are played on directed…

Computer Science and Game Theory · Computer Science 2024-05-14 Zihui Liang , Bakh Khoussainov , Mingyu Xiao

In the tournament game two players, called Maker and Breaker, alternately take turns in claiming an unclaimed edge of the complete graph on n vertices and selecting one of the two possible orientations. Before the game starts, Breaker fixes…

Combinatorics · Mathematics 2019-02-20 Dennis Clemens , Heidi Gebauer , Anita Liebenau

The game of Paintbucket was recently introduced by Amundsen and Erickson. It is played on a rectangular grid of black and white pixels. The players alternately fill in one of their opponent's connected components with their own color, until…

Combinatorics · Mathematics 2024-12-02 Ethan J. Saunders , Peter Selinger
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