Related papers: Vertex Nim played on graphs

In this paper, we analyse a misere tree searching game, where players take turns to guess vertices in a tree with a secret `poisoned' vertex. After each turn, the guessed vertex is removed from the tree and the game continues on the…

We consider a variation of cop vs.\ robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on $V(G)$ and moves according to this fixed distribution. The cop…

The UNIQUE GAMES problem is a central problem in algorithms and complexity theory. Given an instance of UNIQUE GAMES, the STRONG UNIQUE GAMES problem asks to find the largest subset of vertices, such that the UNIQUE GAMES instance induced…

The domatic number of a graph is the maximum number of pairwise disjoint dominating sets admitted by the graph. We introduce a game based around this graph invariant. The domatic number game is played on a graph $G$ by two players, Alice…

We consider games played on graphs with the winning conditions for the players specified as weak-parity conditions. In weak-parity conditions the winner of a play is decided by looking into the set of states appearing in the play, rather…

A large class of Positional Games are defined on the complete graph on $n$ vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given -- usually monotone -- property. Here we…

Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…

We study the m-Eternal Domination problem, which is the following two-player game between a defender and an attacker on a graph: initially, the defender positions k guards on vertices of the graph; the game then proceeds in turns between…

In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In {\em bidding…

In this paper, we consider a modular extension to the game of Nim, which we call $m$-Modular Nim, and explore its optimal strategy. In $m$-Modular Nim, a player can either make a standard Nim move or remove a multiple of $m$ tokens in…

A configuration of a graph is an assignment of one of two states, on or off, to each vertex of it. A regular move at a vertex changes the states of the neighbors of that vertex. A valid move is a regular move at an on vertex. The following…

An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…

We study a new reconfiguration problem inspired by classic mechanical puzzles: a colored token is placed on each vertex of a given graph; we are also given a set of distinguished cycles on the graph. We are tasked with rearranging the…

We analyze a two-player game in which players take turns avoiding the selection of certain points within a convex geometry. The objective is to prevent the convex closure of all chosen points from encompassing a predefined set. The first…

Given a graph $G = (V,E)$, a vertex $u \in V$ ve-dominates all edges incident to any vertex of $N_G[u]$. A set $S \subseteq V$ is a ve-dominating set if for all edges $e\in E$, there exists a vertex $u \in S$ such that $u$ ve-dominates $e$.…

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement against an adversary in uncertain networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious…

The Explorer-Director game, first introduced by Nedev and Muthukrishnan, can be described as a game where two players -- Explorer and Director -- determine the movement of a token on the vertices of a graph. At each time step, the Explorer…

In the tournament game two players, called Maker and Breaker, alternately take turns in claiming an unclaimed edge of the complete graph on n vertices and selecting one of the two possible orientations. Before the game starts, Breaker fixes…

We consider a subtraction Nim with subtraction set {s_1,s_2,s_3={2,4n,4n+2}, where n is a positive integer such that n >= 3. We do not treat the case that n=1 or n=2 in this article. We show that this game satisfies the reverse-mex property…

Subtraction games are a classical topic in Combinatorial Game Theory. A result of Golomb~(1966) shows that every subtraction game with a finite move set has an eventually periodic nim-sequence, but the known proof yields only an exponential…