Related papers: Avoider-Enforcer games played on edge disjoint hyp…
In this paper, we study $(1 : b)$ Avoider-Enforcer games played on the edge set of the complete graph on $n$ vertices. For every constant $k\geq 3$ we analyse the $k$-star game, where Avoider tries to avoid claiming $k$ edges incident to…
In an Avoider-Enforcer game, we are given a hypergraph. Avoider and Enforcer alternate in claiming an unclaimed vertex, until all the vertices of the hypergraph are claimed. Enforcer wins if Avoider claims all vertices of an edge; Avoider…
In the Avoider-Enforcer convention of positional games, two players, Avoider and Enforcer, take turns selecting vertices from a hypergraph H. Enforcer wins if, by the time all vertices of H have been selected, Avoider has completely filled…
We analyze the duration of the unbiased Avoider-Enforcer game for three basic positional games. All the games are played on the edges of the complete graph on $n$ vertices, and Avoider's goal is to keep his graph outerplanar, diamond-free…
In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for…
Given a fixed graph $H$ with at least two edges and positive integers $n$ and $b$, the strict $(1 \colon b)$ Avoider-Enforcer $H$-game, played on the edge set of $K_n$, has the following rules: In each turn Avoider picks exactly one edge,…
In the Avoider-Enforcer game on the complete graph $K_n$, the players (Avoider and Enforcer) each take an edge in turn. Given a graph property $\mathcal{P}$, Enforcer wins the game if Avoider's graph has the property $\mathcal{P}$. An…
Avoidance games are games in which two players claim vertices of a hypergraph and try to avoid some structures. These games are studied since the introduction of the game of SIM in 1968, but only few complexity results are known on them. In…
In this paper we analyze biased Maker-Breaker games and Avoider-Enforcer games, both played on the edge set of a random board $G\sim \gnp$. In Maker-Breaker games there are two players, denoted by Maker and Breaker. In each round, Maker…
We consider biased $(1:b)$ Avoider-Enforcer games in the monotone and strict versions. In particular, we show that Avoider can keep his graph being a forest for every but maybe the last round of the game if $b \geq 200 n \ln n$. By this we…
We introduce a new type of positional games, played on a vertex set of a graph. Given a graph $G$, two players claim vertices of $G$, where the outcome of the game is determined by the subgraphs of $G$ induced by the vertices claimed by…
In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either a single vertex or a hyperedge. When a player chooses to remove one vertex,…
We consider some biased Maker-Breaker games. Starting with the complete $k$-uniform hypergraph on $n$ vertices, at each turn Maker claims one edge, and then Breaker claims $b$ edges. Maker's goal is to obtain a set of edges having some…
The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
Given an increasing graph property $\cal F$, the strong Avoider-Avoider $\cal F$ game is played on the edge set of a complete graph. Two players, Red and Blue, take turns in claiming previously unclaimed edges with Red going first, and the…
We consider three variants of a partisan combinatorial game between two players, Left and Right, played on an undirected simple graph. Left is able to delete vertices (and incident edges) while Right is able to delete edges. This natural…
We study the unbiased WalkerMaker-WalkerBreaker games on the edge set of the complete graph on $n$ vertices, $K_n$, a variant of well-known Maker-Breaker positional games, where both players have the restriction on the way of playing.…
We consider zero-sum games in which players move between adjacent states, where in each pair of adjacent states one state dominates the other. The states in our game can represent positional advantages in physical conflict such as high…
This paper introduced a pursuit and evasion game to be played on a connected graph. One player moves invisibly around the graph, and the other player must guess his position. At each time step the second player guesses a vertex, winning if…
The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of…