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In this paper we analyze biased Maker-Breaker games and Avoider-Enforcer games, both played on the edge set of a random board $G\sim \gnp$. In Maker-Breaker games there are two players, denoted by Maker and Breaker. In each round, Maker…

Combinatorics · Mathematics 2012-10-30 Asaf Ferber , Roman Glebov , Michael Krivelevich , Alon Naor

We consider three variants of a partisan combinatorial game between two players, Left and Right, played on an undirected simple graph. Left is able to delete vertices (and incident edges) while Right is able to delete edges. This natural…

Combinatorics · Mathematics 2021-01-06 Nathan Shank , Devon Vukovich

In the Avoider-Enforcer convention of positional games, two players, Avoider and Enforcer, take turns selecting vertices from a hypergraph H. Enforcer wins if, by the time all vertices of H have been selected, Avoider has completely filled…

Combinatorics · Mathematics 2025-03-28 Florian Galliot , Valentin Gledel , Aline Parreau

We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…

Combinatorics · Mathematics 2024-12-23 Nathan Bowler , Florian Gut

In this paper, we analyse a misere tree searching game, where players take turns to guess vertices in a tree with a secret `poisoned' vertex. After each turn, the guessed vertex is removed from the tree and the game continues on the…

Probability · Mathematics 2025-03-11 Ben Andrews

We study a two-player game played on undirected graphs called {\sc Trail Trap}, which is a variant of a game known as {\sc Partizan Edge Geography}. One player starts by choosing any edge and moving a token from one endpoint to the other;…

A large class of Positional Games are defined on the complete graph on $n$ vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given -- usually monotone -- property. Here we…

Combinatorics · Mathematics 2016-05-24 József Balogh , Ryan R. Martin , András Pluhár

Subset take-away is a two-player game involving a fixed finite set A. Players alternate choosing a proper, non-empty subset of A, with the condition that one may not name a set containing a set that was named earlier. A player unable to…

Combinatorics · Mathematics 2016-05-05 J. Daniel Christensen , Mark Tilford

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

In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either a single vertex or a hyperedge. When a player chooses to remove one vertex,…

Combinatorics · Mathematics 2022-03-21 T. H. Molena

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…

Computer Science and Game Theory · Computer Science 2010-06-09 Julien Cristau , Claire David , Florian Horn

This paper studies a class of approach-evasion differential games, in which one player aims to steer the state of a dynamic system to the given target set in minimum time, while avoiding some set of disallowed states, and the other player…

Optimization and Control · Mathematics 2013-10-01 Erich Mueller , Minghui Zhu , Sertac Karaman , Emilio Frazzoli

The graph grabbing game is played on a non-negatively weighted connected graph by Alice and Bob who alternately claim a non-cut vertex from the remaining graph, where Alice plays first, to maximize the weights on their respective claimed…

Combinatorics · Mathematics 2020-07-24 Sopon Boriboon , Teeradej Kittipassorn

Consider the following one-player game played on an initially empty graph with $n$ vertices. At each stage a randomly selected new edge is added and the player must immediately color the edge with one of $r$ available colors. Her objective…

Combinatorics · Mathematics 2016-03-25 Andreas Noever

A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the subset. The convex hull of a set of vertices is the smallest convex set containing the set. We study…

Combinatorics · Mathematics 2025-05-14 Bret J. Benesh , Dana C. Ernst , Marie Meyer , Sarah K. Salmon , Nandor Sieben

We consider zero-sum games in which players move between adjacent states, where in each pair of adjacent states one state dominates the other. The states in our game can represent positional advantages in physical conflict such as high…

Computer Science and Game Theory · Computer Science 2024-07-11 Farid Arthaud , Edan Orzech , Martin Rinard

Motivated by the controller placement problems in software-defined networks and the fair division principles of classical "cake cutting", we investigate the following two-player zero-sum game. In our model, a defender places a limited…

Computational Complexity · Computer Science 2026-05-19 Grzegorz Gutowski , Konstanty Junosza-Szaniawski , Antonio Lauerbach , Alexander Wolff

In this paper we will be introducing a type of game which as far as this author is aware has never been studied before. These are games where there are two players, one who is trying to get one of his pieces, called a King to a predefined…

Combinatorics · Mathematics 2012-09-07 Fraser Stewart

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 analyze the duration of the unbiased Avoider-Enforcer game for three basic positional games. All the games are played on the edges of the complete graph on $n$ vertices, and Avoider's goal is to keep his graph outerplanar, diamond-free…

Combinatorics · Mathematics 2009-10-26 János Barát , Miloš Stojaković