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Related papers: An evasion game on a graph

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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

Given a graph G with positive integer weights on the vertices, and a token placed on some current vertex u, two players alternately remove a positive integer weight from u and then move the token to a new current vertex adjacent to u. When…

Discrete Mathematics · Computer Science 2012-08-06 Eric Duchêne , Gabriel Renault

We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited before. A player who cannot move loses. We analyze outcomes with…

Probability · Mathematics 2015-05-29 Riddhipratim Basu , Alexander E. Holroyd , James B. Martin , Johan Wästlund

The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of…

Combinatorics · Mathematics 2020-01-29 Mingrui Liu

Graph Exploration problems ask a searcher to explore an unknown environment. The environment is modeled as a graph, where the searcher needs to visit each vertex beginning at some vertex. Treasure Hunt problems are a variation of Graph…

Computational Complexity · Computer Science 2024-12-02 Janosch Fuchs , Christoph Grüne , Tom Janßen

Semi-supervised learning is a popular class of techniques to learn from labeled and unlabeled data. The paper proposes an application of a recently proposed approach of graph transduction that exploits game theoretic notions to the problem…

Computer Vision and Pattern Recognition · Computer Science 2018-06-26 Tewodros Mulugeta Dagnew , Dalia Coppi , Marcello Pelillo , Rita Cucchiara

Motivated by the success of domination games and by a variation of the coloring game called the indicated coloring game, we introduce a version of domination games called the indicated domination game. It is played on an arbitrary graph $G$…

Combinatorics · Mathematics 2024-03-28 Boštjan Brešar , Csilla Bujtás , Vesna Iršič , Douglas F. Rall , Zsolt Tuza

The game of cops and robber is a turn based vertex pursuit game played on a connected graph between a team of cops and a single robber. The cops and the robber move alternately along the edges of the graph. We say the team of cops win the…

Combinatorics · Mathematics 2022-11-30 Uttam K. Gupta , Suchismita Mishra , Dinabandhu Pradhan

The game of cops and robbers is played on a fixed (finite or infinite) graph $G$. The cop chooses his starting position, then the robber chooses his. After that, they take turns and move to adjacent vertices, or stay at their current…

Combinatorics · Mathematics 2025-07-31 Tomáš Flídr , Maria-Romina Ivan

Cops and robbers is a pursuit-evasion game played on graphs. We completely classify the cop numbers for $n \times n$ knight graphs and queen graphs. This completes the classification of the cop numbers for all $n \times n$ classical chess…

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 set. The convex hull of a set of vertices is the smallest convex set containing the set. We study…

Combinatorics · Mathematics 2024-10-17 Bret J. Benesh , Dana C. Ernst , Marie Meyer , Sarah Salmon , Nandor Sieben

The domination game is played on a graph G. Vertices are chosen, one at a time, by two players Dominator and Staller. Each chosen vertex must enlarge the set of vertices of G dominated to that point in the game. Both players use an optimal…

Combinatorics · Mathematics 2013-03-14 Bostjan Bresar , Sandi Klavzar , Douglas F. Rall

We consider the Robber Locating Game, where an invisible moving robber tries to evade the pursuit of one or more helicopter cops, who send distance probes from anywhere on the graph. In this paper, we attempt to propose two useful…

Computational Complexity · Computer Science 2023-07-07 Shiqi Pan

Guessing games for directed graphs were introduced by Riis for studying multiple unicast network coding problems. In a guessing game, the players toss generalised dice and can see some of the other outcomes depending on the structure of an…

Information Theory · Computer Science 2014-11-04 Rahil Baber , Demetres Christofides , Anh N. Dang , Søren Riis , Emil Vaughan

This paper studies a two-person linear-quadratic-Gaussian pursuit-evasion differential game with costly but controlled information. One player can decide when to observe the other player's state. However, one observation of another player's…

Systems and Control · Electrical Eng. & Systems 2022-04-26 Yunhan Huang , Quanyan Zhu

Cops and Robbers is a game played on a graph where a set of cops attempt to capture a single robber. The game proceeds in rounds, where each round first consists of the cops' turn, followed by the robber's turn. In the cops' turn, every cop…

Discrete Mathematics · Computer Science 2025-07-03 Prosenjit Bose , Pat Morin , Karthik Murali

We introduce a new game played on graphs, ``Agents and Adversary". This game is reminiscent of ``Cops and Robbers" but has some fundamental differences. We classify infinite families of graphs as Agents-win and Adversary-win. We then define…

Combinatorics · Mathematics 2026-03-13 William K. Moses , Amanda Redlich , Frederick Stock

We prove new theoretical results about several variations of the cop and robber game on graphs. First, we consider a variation of the cop and robber game which is more symmetric called the cop and killer game. We prove for all $c < 1$ that…

Discrete Mathematics · Computer Science 2017-11-01 Espen Slettnes , Carl Joshua Quines , Shen-Fu Tsai , Jesse Geneson

We consider a game in which a cop searches for a moving robber on a graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph $G$…

Combinatorics · Mathematics 2020-08-12 John Haslegrave , Richard A. B. Johnson , Sebastian Koch

In this paper we analyse two-player games by their response graphs. The response graph has nodes which are strategy profiles, with an arc between profiles if they differ in the strategy of a single player, with the direction of the arc…

Computer Science and Game Theory · Computer Science 2023-02-15 Oliver Biggar , Iman Shames