Related papers: Playing weighted Tron on Trees

The 'Cheating Robot' version of Cops and Robbers is played on a finite, simple, connected graph. The players move in the same time period. However, before moving, the robot observes to which vertices the cops are moving and it is fast…

The domatic game with pallete size $k$ is a $2$-player game played on a graph $G$ recently introduced by Hartnell and Rall. Players Alice and Bob take turns choosing an uncolored vertex from $G$, and coloring it a color from…

Consider an undirected graph modeling a social network, where the vertices represent users, and the edges do connections among them. In the competitive diffusion game, each of a number of players chooses a vertex as a seed to propagate…

Cops and robbers is a game between two players, where one tries to catch the other by moving along the edges of a graph. It is well known that on a finite graph the cop has a winning strategy if and only if the graph is constructible and…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

We consider the following combinatorial two-player game: On the random tree arising from a branching process, each round one player (Breaker) deletes an edge and by that removes the descendant and all its progeny, while the other (Maker)…

This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…

When normal and mis\`{e}re games are played on bi-type binary Galton-Watson trees (with vertices coloured blue or red and each having either no child or precisely $2$ children), with one player allowed to move along monochromatic edges and…

We consider a game in which players are the vertices of a directed graph. Initially, Nature chooses one player according to some fixed distribution and gives her a buck, which represents the request to perform a chore. After completing the…

In the game of $n-Sim$, two players take it in turn to claim unclaimed edges from a complete graph on $n$ vertices, with the first person to create a triangle in his own edges being the loser. We present some strategy-stealing arguments…

Let $n, k$ be positive integers. The $(k+1)$-star avoidance game on $K_n$ is played as follows. Two players take it in turn to claim a (previously unclaimed) edge of the complete graph on $n$ vertices. The first player to claim all edges of…

We study the two-player safe game of Competitive Diffusion, a game-theoretic model for the diffusion of technologies or influence through a social network. In game theory, safe strategies are mixed strategies with a minimal expected gain…

We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…

\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…

A treedepth decomposition of an undirected graph $G$ is a rooted forest $F$ on the vertex set of $G$ such that every edge $uv\in E(G)$ is in ancestor-descendant relationship in $F$. Given a weight function $w\colon V(G)\rightarrow…

We consider the game of Cops and Robber played on the Cartesian product of two trees. Assuming the players play perfectly, it is shown that if there are two cops in the game, then the length of the game (known as the 2-capture time of the…

Motivated by the burning and cooling processes, the burning game is introduced. The game is played on a graph $G$ by the two players (Burner and Staller) that take turns selecting vertices of $G$ to burn; as in the burning process, burning…

This paper proposes a new lens for studying threshold games played on networks when the thresholds are heterogeneous. These are games where agents have two possible actions, and prefer action 1 if and only if enough of their neighbours…

Zero forcing is a combinatorial game played on a graph with the ultimate goal of changing the colour of all the vertices at minimal cost. Originally this game was conceived as a one player game, but later a two-player version was devised…

We introduce the game INFLUENCE, a scoring combinatorial game, played on a directed graph where each vertex is either colored black or white. The two players, Black and White play alternately by taking a vertex of their color and all its…