Related papers: Maker Breaker on Digraphs
We discuss the recently introduced concept of k-in-out graphs, and provide a construction for k-in-out graphs for any positive integer k. We derive a lower bound for the number of vertices of a k-in-out graph for any positive integer k, and…
Token ring topology has been frequently used in the design of distributed loop computer networks and one measure of its performance is the diameter. We propose an algorithm for constructing hamiltonian graphs with $n$ vertices and maximum…
Motivated by its relation to the length of cutting plane proofs for the Maximum Biclique problem, we consider the following communication game on a given graph G, known to both players. Let K be the maximal number of vertices in a complete…
In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
A $k$-matching $M$ of a graph $G=(V,E)$ is a subset $M\subseteq E$ such that each connected component in the subgraph $F = (V,M)$ of $G$ is either a single-vertex graph or $k$-regular, i.e., each vertex has degree $k$. In this contribution,…
In multiplayer games with sequential decision-making, self-interested players form dynamic coalitions to achieve most-preferred temporal goals beyond their individual capabilities. We introduce a novel procedure to synthesize strategies…
Artificial intelligence and robotic competitions are accompanied by a class of game paradigms in which each player privately commits a strategy to a game system which simulates the game using the collected joint strategy and then returns…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
We construct a diffusion approximation of a repeated game in which agents make bets on outcomes of i.i.d. random vectors and their strategies are close to an asymptotically optimal strategy. This model can be interpreted as trading in an…
Motivated by problems in percolation theory, we study the following 2-player positional game. Let $\Lambda_{m \times n}$ be a rectangular grid-graph with $m$ vertices in each row and $n$ vertices in each column. Two players, Maker and…
Graphon games have been introduced to study games with many players who interact through a weighted graph of interaction. By passing to the limit, a game with a continuum of players is obtained, in which the interactions are through a…
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 the $(G,H)$-isomorphism game, a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either $G$ or $H$, whose aim is to convince the verifier that two graphs $G$…
This paper extends and generalizes the well-known cut-matching game framework and provides a novel cut-strategy that produces constant-hop expanders. Constant-hop expanders are a significant strengthening of regular expanders with the…
We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model…
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…
We study a variant of the Cops and Robbers game on graphs in which the robbers damage the visited vertices, aiming to maximize the number of damaged vertices. For that game with one cop against $s$ robbers a conjecture was made by Carlson,…
We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex…
Consider the following game played by two players, called Waiter and Client, on the edges of $K_n$ (where $n$ is divisible by $3$). Initially, all the edges are unclaimed. In each round, Waiter picks two yet unclaimed edges. Client then…