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Motivated by dynamic graph visualization, we study the problem of representing a graph $G$ in the form of a \emph{storyplan}, that is, a sequence of frames with the following properties. Each frame is a planar drawing of the subgraph of $G$…

We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by occupying the same vertex as the robber, they now win by…

The Honey-Bee game is a two-player board game that is played on a connected hexagonal colored grid or (in a generalized setting) on a connected graph with colored nodes. In a single move, a player calls a color and thereby conquers all the…

Computer Science and Game Theory · Computer Science 2011-02-16 Rudolf Fleischer , Gerhard J. Woeginger

We compare two kinds of pursuit-evasion games played on graphs. In Cops and Robbers, the cops can move strategically to adjacent vertices as they please, while in a new variant, called deterministic Zombies and Survivors, the zombies (the…

Combinatorics · Mathematics 2018-09-11 David Offner , Kerry Ojakian

In this short note we consider a variation of the connectivity Waiter-Client game $WC(n,q,\mathcal{A})$ played on an $n$-vertex graph $G$ which consists of $q+1$ disjoint spanning trees. In this game in each round Waiter offers Client $q+1$…

Combinatorics · Mathematics 2015-10-21 Sylwia Antoniuk , Codruut Grosu , Lothar Narins

The domination game is played on a graph $G$ by two players, named Dominator and Staller. They alternatively select vertices of $G$ such that each chosen vertex enlarges the set of vertices dominated before the move on it. Dominator's goal…

Combinatorics · Mathematics 2013-07-23 Boštjan Brešar , Paul Dorbec , Sandi Klavžar , Gašper Košmrlj

A rank-3 Maker-Breaker game is played on a hypergraph in which all hyperedges are sets of at most 3 vertices. The two players of the game, called Maker and Breaker, move alternately. On his turn, maker chooses a vertex to be withdrawn from…

Computational Complexity · Computer Science 2022-09-23 Lear Bahack

Liminal burning generalizes both the burning and cooling processes in graphs. In $k$-liminal burning, a Saboteur reveals $k$-sets of vertices in each round, with the goal of extending the length of the game, and the Arsonist must choose…

Combinatorics · Mathematics 2025-05-19 Anthony Bonato , Trent G. Marbach , John Marcoux , Teddy Mishura

An alternating graph is a directed graph whose vertex set is partitioned into two classes, existential and universal. This forms the basic arena for a plethora of infinite duration two-player games where Player~$\square$ and~$\ocircle$…

Data Structures and Algorithms · Computer Science 2025-08-14 Carlo Comin , Romeo Rizzi

Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours. The game ends once…

Combinatorics · Mathematics 2023-06-22 Dominique Andres , Edwin Lock

The localization game is a variant of the game of Cops and Robber in which the robber is invisible and moves between adjacent vertices, but the cops can probe any $k$ vertices of the graph to obtain the distance between probed vertices and…

Combinatorics · Mathematics 2026-02-10 Vesna Iršič Chenoweth , Matija Skrt

We study Maker/Breaker games on the edges of the complete graph, as introduced by Chvatal and Erdos. We show that in the (m:b) clique game played on K_{N}, the complete graph on N vertices, Maker can achieve a K_{q} for q = (m/(log_{2}(b +…

Computer Science and Game Theory · Computer Science 2009-09-25 Heidi Gebauer

The Cops and Robber game is played on undirected finite graphs. $k$ cops and one robber are positioned on vertices and take turn in moving along edges. The cops win if, after a move, a cop and the robber are on the same vertex. A graph is…

Combinatorics · Mathematics 2011-11-10 Dirk Oliver Theis

We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of…

Physics and Society · Physics 2019-02-20 Shubham Pandey , Reimer Kuehn

We consider the cops and robber game variant consisting of one cop and one robber on time-varying graphs (TVG). The considered TVGs are edge periodic graphs, i.e., for each edge, a binary string $s_e$ determines in which time step the edge…

Computational Complexity · Computer Science 2021-07-13 Nils Morawietz , Petra Wolf

We investigate a new oriented variant of the Firefighter Problem. In the traditional Firefighter Problem, a fire breaks out at a given vertex of a graph, and at each time interval spreads to neighbouring vertices that have not been…

Discrete Mathematics · Computer Science 2015-06-25 Julien Bensmail , Nick Brettell

Motivated by a biological scenario illustrated in the YouTube video \url{ https://www.youtube.com/watch?v=Z_mXDvZQ6dU} where a neutrophil chases a bacteria cell moving in random directions, we present a variant of the cop and robber game on…

Combinatorics · Mathematics 2020-04-02 Pamela Harris , Erik Insko , Alicia Prieto-Langarica , Rade Stoisavljevic , Shaun Sullivan

This research considers Bayesian decision-analytic approaches toward the traversal of an uncertain graph. Namely, a traveler progresses over a graph in which rewards are gained upon a node's first visit and costs are incurred for every edge…

Artificial Intelligence · Computer Science 2025-03-11 William N. Caballero , Phillip R. Jenkins , David Banks , Matthew Robbins

The concept of intransitiveness for games, which is the condition for which there is no first-player winning strategy can arise surprisingly, as happens in the Penney game, an extension of the heads or tails. Since a game can be converted…

Physics and Society · Physics 2024-03-07 Alberto Baldi , Franco Bagnoli

Lights Out is a game played on a graph $G$ where every vertex has a light bulb that is either on or off, and pressing a vertex $v$ toggles the state of every vertex in the closed neighborhood of $v$. The goal is to find a subset of vertices…

Combinatorics · Mathematics 2026-02-10 Julien Codsi , Sergio Cristancho , Alexander Divoux , Varun Sivashankar