Related papers: Some Maker-Breaker games on hypergraphs
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…
A multi-graph $G$ on $n$ vertices is $(k,\ell)$-sparse if every subset of $n'\leq n$ vertices spans at most $kn'- \ell$ edges. $G$ is {\em tight} if, in addition, it has exactly $kn - \ell$ edges. For integer values $k$ and $\ell \in [0,…
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…
We analyze Avoider-Enforcer games played on edge disjoint hypergraphs, providing an analog of the classic and well known game $Box$, due to Chv\'{a}tal and Erd\H{o}s. We consider both strict and monotone versions of Avoider-Enforcer games,…
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…
In an influential paper, Erd\H{o}s and Selfridge introduced the Maker-Breaker game played on a hypergraph, or equivalently, on a monotone CNF. The players take turns assigning values to variables of their choosing, and Breaker's goal is to…
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…
The online Ramsey turnaround game is a game between two players, Builder and Painter, on a board of $n$ vertices using $3$ colors, for a fixed graph $H$ on at most $n$ vertices. The goal of Painter is to force a monochromatic copy of $H$,…
The $k$-cap (or $k$-winners-take-all) process on a graph works as follows: in each iteration, exactly $k$ vertices of the graph are in the cap (i.e., winners); the next round winners are the vertices that have the highest total degree to…
We study the Maker-Breaker domination game played by Dominator and Staller on the vertex set of a given graph. Dominator wins when the vertices he has claimed form a dominating set of the graph. Staller wins if she makes it impossible for…
This work is concerned with the study of the Game of Graph Nim -- a class of two-player combinatorial games -- on graphs with $4$ edges. To each edge of such a graph is assigned a positive-integer-valued edge-weight, and during each round…
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 $G$.…
We introduce a model involving two adversaries Buster and Fixer taking turns modifying a connected graph, where each round consists of Buster deleting a subset of edges and Fixer responding by adding edges from a finite reserve set of…
An oriented k-uniform hypergraph (a family of ordered k-sets) has the ordering property (or Property O) if for every linear order of the vertex set, there is some edge oriented consistently with the linear order. We find bounds on the…
We consider the following budget-constrained random graph process introduced by Frieze, Krivelevich and Michaeli. A player, called Builder, is presented with $t$ distinct edges of $K_n$ one by one, chosen uniformly at random. Builder may…
We study two types of two player, perfect information games with no chance moves, played on the edge set of the binomial random graph ${\mathcal G}(n,p)$. In each round of the $(1 : q)$ Waiter-Client Hamiltonicity game, the first player,…
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…
Consider the following two-player game on the edges of $K_n$, the complete graph with $n$ vertices: Starting with an empty graph $G$ on the vertex set of $K_n$, in each round the first player chooses $b \in \mathbb{N}$ edges from $K_n$…
The \emph{slow-coloring game} is played by Lister and Painter on a graph $G$. Initially, all vertices of $G$ are uncolored. In each round, Lister marks a nonempty set $M$ of uncolored vertices, and Painter colors a subset of $M$ that is…
We study two games proposed by Erd\H{o}s, and one game by Bensmail and Mc Inerney, all sharing a common setup: two players alternately colour edges of a complete graph, or in the biased version, they colour $p$ and $q$ edges respectively on…