Related papers: Digraph Placement Games

We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a back-action on the causal…

Cram, Domineering, and Arc Kayles are well-studied combinatorial games. They are interpreted as edge-selecting-type games on graphs, and the selected edges during a game form a matching. In this paper, we define a generalized game called…

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…

A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population…

A Subtraction-Division game is a two player combinatorial game with three parameters: a set S, a set D, and a number n. The game starts at n, and is a race to say the number 1. Each player, on their turn, can either move the total to n-s…

The total isolation game is played on a graph $G$ by two players who take turns playing a vertex such that if $S$ is the set of already played vertices, then a vertex can be selected only if it is adjacent to a vertex that belongs to a…

We consider monotonicity problems for graph searching games. Variants of these games - defined by the type of moves allowed for the players - have been found to be closely connected to graph decompositions and associated width measures such…

A graph $G = (V,E)$ is said to be saturated with respect to a monotone increasing graph property ${\mathcal P}$, if $G \notin {\mathcal P}$ but $G \cup \{e\} \in {\mathcal P}$ for every $e \in \binom{V}{2} \setminus E$. The saturation game…

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…

Graph burning is a discrete-time process that models the spread of influence in a network. Vertices are either burning or unburned, and in each round, a burning vertex causes all of its neighbours to become burning before a new fire source…

We examine short combinatorial games for three or more players under a new play convention in which a player who cannot move on their turn is the unique loser. We show that many theorems of impartial and partizan two-player games under…

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…

A proper edge $t$-coloring of a graph $G$ is a coloring of edges of $G$ with colors $1,2,...,t$ such that all colors are used, and no two adjacent edges receive the same color. The set of colors of edges incident with a vertex $x$ is called…

Poset games are a class of combinatorial game that remain unsolved. Soltys and Wilson proved that computing wining strategies is in \textbf{PSPACE} and aside from special cases such as Nim and N-Free games, \textbf{P} time algorithms for…

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…

The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between two distinct vertices $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x,v)$ and…

We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…

In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453--1462], where the players Dominator and Staller alternately select vertices of $G$. Each vertex chosen must…

Given a c-colored graph G, a vertex of G is happy if it has the same color as all its neighbors. The notion of happy vertices was introduced by Zhang and Li to compute the homophily of a graph. Eto, et al. introduced the Maker-Maker version…

Consider a system in which players at nodes of an underlying graph G repeatedly play Prisoner's Dilemma against their neighbors. The players adapt their strategies based on the past behavior of their opponents by applying the so-called…