Related papers: Solving Maker-Breaker Games on 5-uniform hypergrap…
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 combine the ideas of edge coloring games and asymmetric graph coloring games and define the \emph{$(m,1)$-edge coloring game}, which is alternatively played by two players Maker and Breaker on a finite simple graph $G$ with a set of…
Recently the matcher game was introduced. In this game, two players create a maximal matching by one player repeatedly choosing a vertex and the other player choosing a $K_2$ containing that vertex. One player tries to minimize the result…
A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…
In the vertex colouring game on a graph $G$, Maker and Breaker alternately colour vertices of $G$ from a palette of $k$ colours, with no two adjacent vertices allowed the same colour. Maker seeks to colour the whole graph while Breaker…
We study routing games where every agent sequentially decides her next edge when she obtains the green light at each vertex. Because every edge only has capacity to let out one agent per round, an edge acts as a FIFO waiting queue that…
We introduce and study two Maker-Breaker-like games for constructing planar graphs: the edge drawing game, where two players take turns drawing non-intersecting edges between points in the plane, and the circle packing game, where the…
A perfect matching in a hypergraph is a set of edges that partition the set of vertices. We study the complexity of deciding the existence of a perfect matching in orderable and separable hypergraphs. We show that the class of orderable…
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…
Given a class $\mathcal{C}$ of graphs and a fixed graph $H$, the online Ramsey game for $H$ on $\mathcal C$ is a game between two players Builder and Painter as follows: an unbounded set of vertices is given as an initial state, and on each…
We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the…
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…
This paper considers a game in which a single cop and a single robber take turns moving along the edges of a given graph $G$. If there exists a strategy for the cop which enables it to be positioned at the same vertex as the robber…
A $d$-defective $k$-painting game on a graph $G$ is played by two players: Lister and Painter. Initially, each vertex is uncolored and has $k$ tokens. In each round, Lister marks a chosen set $M$ of uncolored vertices and removes one token…
We consider a cops and robber game where the cops are blocking edges of a graph, while the robber occupies its vertices. At each round of the game, the cops choose some set of edges to block and right after the robber is obliged to move to…
For a positive integer $k$ we consider the $k$-vertex-connectivity game, played on the edge set of $K_n$, the complete graph on $n$ vertices. We first study the Maker-Breaker version of this game and prove that, for any integer $k \geq 2$…
We consider the following two-player game, parametrised by positive integers $n$ and $k$. The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on $n$…
Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value…
We introduce the rendezvous game with adversaries. In this game, two players, {\sl Facilitator} and {\sl Disruptor}, play against each other on a graph. Facilitator has two agents, and Disruptor has a team of $k$ agents located in some…
In a $(1:b)$ biased Maker-Breaker game, how good a strategy is for a player can be measured by the bias range for which its rival can win, choosing an appropriate counterstrategy. Bednarska and {\L}uczak proved that, in the $H$-subgraph…