Related papers: Chomp on Graphs and Subsets

This paper introduced a pursuit and evasion game to be played on a connected graph. One player moves invisibly around the graph, and the other player must guess his position. At each time step the second player guesses a vertex, winning if…

This work is concerned with the study of the Game of Graph Nim -- a class of two-player combinatorial games -- on graphs with $4$ edges. To each edge of such a graph is assigned a positive-integer-valued edge-weight, and during each round…

In the game of Graph Nimors, two players alternately perform graph minor operations (deletion and contraction of edges) on a graph until no edges remain, at which point the player who last moved wins. We present theoretical and experimental…

A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is adjacent to some other edges appeared previously. In this paper, we focus on complete bipartite…

We introduce Shortest Connection Game, a two-player game played on a directed graph with edge costs. Given two designated vertices in which they start, the players take turns in choosing edges emanating from the vertex they are currently…

We investigate extremal graphs related to the game of Cops and Robbers. We focus on graphs where a single cop can catch the robber; such graphs are called cop-win. The capture time of a cop-win graph is the minimum number of moves the cop…

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

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…

In the graph sharing game, two players share a connected graph $G$ with non-negative weights assigned to the vertices, claiming and collecting the vertices of $G$ one by one, while keeping the set of all claimed vertices connected through…

\textsc{Cops and Robber} is a game played on graphs where a set of \textit{cops} aim to \textit{capture} the position of a single \textit{robber}. The main parameter of interest in this game is the \textit{cop number}, which is the minimum…

We propose a class of two person perfect information games based on weighted graphs. One of these games can be described in terms of a round pizza which is cut radially into pieces of varying size. The two players alternately take pieces…

Snake is a classic computer game, which has been around for decades. Based on this game, we study the game of Snake on arbitrary undirected graphs. A snake forms a simple path that has to move to an apple while avoiding colliding with…

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;…

The two-player, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and…

Placement games are a subclass of combinatorial games which are played on graphs. We will demonstrate that one can construct simplicial complexes corresponding to a placement game, and this game could be considered as a game played on these…

The dollar game is a chip-firing game introduced by Baker and Norine (2007) as a context in which to formulate and prove the Riemann-Roch theorem for graphs. A divisor on a graph is a formal integer sum of vertices. Each determines a dollar…

In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…

We define a new escape game in graphs that we call Nemesis. The game is played on a graph having a subset of vertices labeled as exits and the goal of one of the two players, called the fugitive, is to reach one of these exit vertices. The…

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…

Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of $G$ are…