Related papers: Connected Subtraction Games on Subdivided Stars
A pebbling move refers to the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The goal of graph pebbling is: Given an initial distribution of pebbles, use pebbling moves to reach a specified goal…
An alternating graph is a directed graph whose vertex set is partitioned into two classes, existential and universal. This forms the basic arena for a plethora of infinite duration two-player games where Player~$\square$ and~$\ocircle$…
We present the notion of separable game with respect to a forward directed hypergraph (FDH-graph), which refines and generalizes that of graphical game. First, we show that there exists a minimal FDH-graph with respect to which a game is…
Graph pebbling is a game played on a connected graph G. A player purchases pebbles at a dollar a piece, and hands them to an adversary who distributes them among the vertices of G (called a configuration) and chooses a target vertex r. The…
The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of…
The two-player, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and…
The game of Cops and Robber is a pursuit-evasion game which is usually played on a connected graph. In the game, a set of cops and a robber move around the vertices of a graph along edges, where the cops aim to capture the robber, while the…
The (total) connected domination game on a graph $G$ is played by two players, Dominator and Staller, according to the standard (total) domination game with the additional requirement that at each stage of the game the selected vertices…
We introduce a new combinatorial game, named Triangle Game. In this game, a directed $3$-cycle graph is given, and tokens are placed on each vertex. The player chooses an edge and takes at least one token from the initial vertex. At the…
A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble…
We introduce the game of Cat Herding, where an omnipresent herder slowly cuts down a graph until an evasive cat player has nowhere to go. The number of cuts made is the score of a game, and we study the score under optimal play. In this…
For a graph G, a monotone increasing graph property P and positive integer q, we define the Client-Waiter game to be a two-player game which runs as follows. In each turn Waiter is offering Client a subset of at least one and at most q+1…
This paper studies a stochastic game theoretic approach to security and intrusion detection in communication and computer networks. Specifically, an Attacker and a Defender take part in a two-player game over a network of nodes whose…
Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to…
Motivated by the controller placement problems in software-defined networks and the fair division principles of classical "cake cutting", we investigate the following two-player zero-sum game. In our model, a defender places a limited…
We develop an algorithm for efficiently computing recursively defined functions on posets. We illustrate this algorithm by disproving conjectures about the game Subset Takeaway (Chomp on a hypercube) and computing the number of linear…
We study a variant of the classical cop-robber game played on compact metric graphs, where each edge is assigned a positive length and identified with a real interval of corresponding length. In this setting, both the cop and the robber…
A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…
In this paper, we study a family of take-away games called $\alpha$-tag, parametrized by a real number $\alpha\ge 1$. We show that for any given $\alpha$, there is a half-open interval $I_\alpha$ containing $\alpha$ such that the set of…
The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the location of the robber. We present a novel graph parameter called…