Related papers: Spanning Structures in Walker--Breaker Games

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…

In chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning strategy? Can a explicit…

The rook graph is a graph whose edges represent all the possible legal moves of the rook chess piece on a chessboard. The problem we consider is the following. Given any set $M$ containing pairs of cells such that each cell of the $m_1…

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;…

We consider a Maker-Breaker type game on the plane, in which each player takes $t$ points on their $t^\textrm{th}$ turn. Maker wins if he obtains $n$ points on a line (in any direction) without any of Breaker's points between them. We show…

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 $G$…

We study the Maker-Breaker game on the hypergraph of chains of fixed size in a poset. In a product of chains, the maximum size of a chain that Maker can guarantee building is $k-\lfloor r/2\rfloor$, where $k$ is the maximum size of a chain…

Two-player graph games are a fundamental model for reasoning about the interaction of agents. These games are played between two players who move a token along a graph. In bidding games, the players have some monetary budget, and at each…

Given an integer-valued matrix $A$ of dimension $\ell \times k$ and an integer-valued vector $b$ of dimension $\ell$, the Maker-Breaker $(A,b)$-game on a set of integers $X$ is the game where Maker and Breaker take turns claiming previously…

We study the $(m,b)$ Maker-Breaker percolation game on $\mathbb{Z}^2$, introduced by Day and Falgas-Ravry. As our first result, we show that Breaker has a winning strategy for the $(m,b)$-game whenever $b \geq (2-\frac{1}{14} + o(1))m$,…

A graph is Hamiltonian if it contains a cycle which passes through every vertex of the graph exactly once. A classical theorem of Dirac from 1952 asserts that every graph on $n$ vertices with minimum degree at least $n/2$ is Hamiltonian. We…

Let $G$ be a graph with vertex set $V$. A set $S \subseteq V$ is a \emph{strong resolving set} of $G$ if, for distinct $x,y\in V$, there exists $z\in S$ such that either $x$ lies on a $y-z$ geodesic or $y$ lies on an $x-z$ geodesic in $G$.…

For a positive integer $n$ and a tree $T_n$ on $n$ vertices, we consider an unbiased Waiter-Client game $\textrm{WC}(n,T_n)$ played on the complete graph~$K_n$, in which Waiter's goal is to force Client to build a copy of $T_n$. We prove…

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…

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…

The graph grabbing game is played on a non-negatively weighted connected graph by Alice and Bob who alternately claim a non-cut vertex from the remaining graph, where Alice plays first, to maximize the weights on their respective claimed…

We introduce a general framework for positional games in which players score points by claiming a prescribed portion of each winning set, extending the notion of scoring Maker-Breaker games. In the scoring variant, Maker gains a point by…

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…

We study the following game version of the generalized graph Tur\'an problem. For two fixed graphs $F$ and $H$, two players, Constructor and Blocker, alternately claim unclaimed edges of the complete graph $K_n$. Constructor can only claim…

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~$\ocircle$…