Related papers: A generalization of Arc-Kayles

We study the computational complexity of distance games, a class of combinatorial games played on graphs. A move consists of colouring an uncoloured vertex subject to it not being at certain distances determined by two sets, D and S. D is…

In 2021, Adam Zsolt Wagner proposed an approach to disprove conjectures in graph theory using Reinforcement Learning (RL). Wagner's idea can be framed as follows: consider a conjecture, such as a certain quantity f(G) < 0 for every graph G;…

We consider the linearized Korteweg-de-Vries equa- tions, sometimes called Airy equation, on general metric graphs with edge lengths bounded away from zero. We show that pro- perties of the induced dynamics can be obtained by studying…

The $(m,b)$ Maker-Breaker percolation game on $(\mathbb{Z}^2)_p$, introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of $\mathbb{Z}^2$ is removed independently with probability $1-p$. After…

We study competition on scale-free random graphs, where the degree distribution satisfies an asymptotic power-law with infinite variance. Our competition process is such that the two types attempt at occupying vertices incident to the…

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…

Waiter-Client and Client-Waiter games are two-player, perfect information games, with no chance moves, played on a finite set (board) with special subsets known as the winning sets. Each round of the biased $(1:q)$ game begins with Waiter…

The game of Cat Herding is one in which cat and herder players alternate turns, with the evasive cat moving along non-trivial paths between vertices, and the herder deleting single edges from the graph. Eventually the cat cannot move, and…

Uncover the vertices of a given graph, deterministic or random, in random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization…

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…

In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns…

In this paper we will be introducing a type of game which as far as this author is aware has never been studied before. These are games where there are two players, one who is trying to get one of his pieces, called a King to a predefined…

We show that the winning positions of a certain type of two-player game form interesting patterns which often defy analysis, yet can be computed by a cellular automaton. The game, known as {\em Blocking Wythoff Nim}, consists of moving a…

The goal is to show that an edge-reinforced random walk on a graph of bounded degree, with reinforcement weight function $W$ taken from a general class of reciprocally summable reinforcement weight functions, traverses a random attracting…

We study the positional game where two players, Maker and Breaker, alternately select respectively $1$ and $b$ previously unclaimed edges of $K_n$. Maker wins if she succeeds in claiming all edges of some odd cycle in $K_n$ and Breaker wins…

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…

In this paper, we study a variant of the classical Wythoff's game. The classical form is played with two piles of stones, from which two players take turns to remove stones from one or both piles. When removing stones from both piles, an…

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…

Consider the balanced Ramsey game, in which a player has r colors and where in each step r random edges of an initially empty graph on n vertices are presented. The player has to immediately assign a different color to each edge and her…

Fix two integers $n, k$, with $n$ divisible by $k$, and consider the following game played by two players, Waiter and Client, on the edges of $K_n$. Starting with all the edges marked as unclaimed, in each round, Waiter picks two yet…