Related papers: The random strategy in Maker-Breaker graph minor g…
We investigate the game of cops and robber, played on a finite graph, between one cop and one robber. If the cop can force a win on a graph, the graph is called cop-win. We describe a procedure we call corner ranking, performed on a graph,…
Decoding strategies play a pivotal role in text generation for modern language models, yet a puzzling gap divides theory and practice. Surprisingly, strategies that should intuitively be optimal, such as Maximum a Posteriori (MAP), often…
In the Maker-Breaker domination game played on a graph $G$, Dominator's goal is to select a dominating set and Staller's goal is to claim a closed neighborhood of some vertex. We study the cases when Staller can win the game. If Dominator…
We look at the unbiased Maker-Breaker Hamiltonicity game played on the edge set of a complete graph $K_n$, where Maker's goal is to claim a Hamiltonian cycle. First, we prove that, independent of who starts, Maker can win the game for $n =…
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…
We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…
We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph. We say a player fills an edge if that player has picked all…
Waiter-Client games are played on some hypergraph $(X,\mathcal{F})$, where $\mathcal{F}$ denotes the family of winning sets. For some bias $b$, during each round of such a game Waiter offers to Client $b+1$ elements of $X$, of which Client…
We study concurrent stochastic reachability games played on finite graphs. Two players, Max and Min, seek respectively to maximize and minimize the probability of reaching a set of target states. We prove that Max has a memoryless strategy…
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…
We consider a dynamic model for competition in a social network, where two strategic agents have fixed beliefs and the non-strategic/regular agents adjust their states according to a distributed consensus protocol. We suppose that one…
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…
We consider evolutionary games on a population whose underlying topology of interactions is determined by a binomial random graph $G(n,p)$. Our focus is on 2-player symmetric games with 2 strategies played between the incident members of…
In the Maker-Breaker domination game, Dominator and Staller play on a graph $G$ by taking turns in which each player selects a not yet played vertex of $G$. Dominator's goal is to select all the vertices in a dominating set, while Staller…
Baker devised a technique to obtain approximation schemes for many optimization problems restricted to planar graphs; her technique was later extended to more general graph classes. In particular, using the Baker's technique and the minor…
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…
The game of \emph{Cops and Robber} is usually played on a graph, where a group of cops attempt to catch a robber moving along the edges of the graph. The \emph{cop number} of a graph is the minimum number of cops required to win the game.…
Given a tree $T=(V,E)$ on $n$ vertices, we consider the $(1 : q)$ Maker-Breaker tree embedding game ${\mathcal T}_n$. The board of this game is the edge set of the complete graph on $n$ vertices. Maker wins ${\mathcal T}_n$ if and only if…
A predominated graph is a pair $(G,D)$, where $G$ is a graph and the vertices in $D\subseteq V(G)$ are considered already dominated. Maker-Breaker domination game critical (MBD critical) predominated graphs are introduced as the…
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…