Related papers: The Maker-Breaker Largest Connected Subgraph Game
The graph coloring game is a two-player game in which, given a graph G and a set of k colors, the two players, Alice and Bob, take turns coloring properly an uncolored vertex of G, Alice having the first move. Alice wins the game if and…
The graph coloring game is a famous two-player game (re)introduced by Bodlaender in $1991$. Given a graph $G$ and $k \in \mathbb{N}$, Alice and Bob alternately (starting with Alice) color an uncolored vertex with some color in…
Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours. The game ends once…
We study the following combinatorial game played by two players, Alice and Bob, which generalizes the Pizza game considered by Brown, Winkler and others. Given a connected graph G with nonnegative weights assigned to its vertices, the…
The $[X,Y]$-edge colouring game is played with a set of $k$ colours on a graph $G$ with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player $X\in\{A,B\}$ has the first move.…
We study the two-player game where Maker and Breaker alternately color the edges of a given graph $G$ with $k$ colors such that adjacent edges never get the same color. Maker's goal is to play such that at the end of the game, all edges are…
In the $\left(1:b\right)$ component game played on a graph $G$, two players, Maker and Breaker, alternately claim~$1$ and~$b$ previously unclaimed edges of $G$, respectively. Maker's aim is to maximise the size of a largest connected…
In this paper, we construct two hypergraphs which exhibit the following properties. We first construct a hypergraph $G_{CP}$ and show that Breaker wins the Maker-Breaker game on $G_{CP}$, but Chooser wins the Chooser-Picker game on…
Maker-Breaker total domination game in graphs is introduced as a natural counterpart to the Maker-Breaker domination game recently studied by Duch\^ene, Gledel, Parreau, and Renault. Both games are instances of the combinatorial…
A set of vertices $W$ of a graph $G$ is a resolving set if every vertex of $G$ is uniquely determined by its vector of distances to $W$. In this paper, the Maker-Breaker resolving game is introduced. The game is played on a graph $G$ by…
We investigate a variation of the graph coloring game, as studied in [2]. In the original coloring game, two players, Alice and Bob, alternate coloring vertices on a graph with legal colors from a fixed color set, where a color {\alpha} is…
We study the algorithmic complexity of Maker-Breaker games played on the edge sets of general graphs. We mainly consider the perfect matching game and the $H$-game. Maker wins if she claims the edges of a perfect matching in the first, and…
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 a Maker-Breaker game on a graph $G$, Breaker and Maker alternately claim edges of $G$. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games…
Given a graph $G$ and a list assignment $L$ for $G$, the indicated $L$-colouring game on $G$ is played by two players: Ann and Ben. In each round, Ann chooses an uncoloured vertex $v$, and Ben colours $v$ with a colour from $L(v)$ that is…
If $k\geq 0$, then a $k$-edge-coloring of a graph $G$ is an assignment of colors to edges of $G$ from the set of $k$ colors, so that adjacent edges receive different colors. A $k$-edge-colorable subgraph of $G$ is maximum if it is the…
Let $(X, \mathcal{F})$ be a hypergraph. The Maker-Breaker game on $(X, \mathcal{F})$ is a combinatorial game between two players, Maker and Breaker. Beginning with Maker, the players take turns claiming vertices from $X$ that have not yet…
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…
Maker-Breaker subgraph games are among the most famous combinatorial games. For given $n,q \in \mathbb{N}$ and a subgraph $C$ of the complete graph $K_n$, the two players, called Maker and Breaker, alternately claim edges of $K_n$. In each…
We study a recently introduced two-person combinatorial game, the $(a,b)$-monochromatic clique transversal game which is played by Alice and Bob on a graph $G$. As we observe, this game is equivalent to the $(b,a)$-biased Maker-Breaker game…