Related papers: The Complexity of Node Blocking for Dags
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…
We introduce Shortest Connection Game, a two-player game played on a directed graph with edge costs. Given two designated vertices in which they start, the players take turns in choosing edges emanating from the vertex they are currently…
Snake is a classic computer game, which has been around for decades. Based on this game, we study the game of Snake on arbitrary undirected graphs. A snake forms a simple path that has to move to an apple while avoiding colliding with…
We examine a dynamic model for the disruption of information flow in hierarchical social networks by considering the vertex-pursuit game Seepage played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block the movement of…
Identifying shortest paths between nodes in a network is an important task in many applications. Recent work has shown that a malicious actor can manipulate a graph to make traffic between two nodes of interest follow their target path. In…
We consider a bandit problem over a graph where the rewards are not directly observed. Instead, the decision maker can compare two nodes and receive (stochastic) information pertaining to the difference in their value. The graph structure…
We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a…
A game-theoretic model for the study of dynamic networks is analyzed. The model is motivated by communication networks that are subject to failure of nodes and where the restoration needs resources. The corresponding two-player game is…
We analyze Solo Chess puzzles, where the input is an $n \times n$ board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves to reduce down to a single piece. Prior work analyzes this…
A Stackelberg Vertex Cover game is played on an undirected graph $\mathcal{G}$ where some of the vertices are under the control of a \emph{leader}. The remaining vertices are assigned a fixed weight. The game is played in two stages. First,…
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…
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…
A vertex $u$ in a graph $G$ totally dominates a vertex $v$ if $u$ is adjacent to $v$ in $G$. A total dominating set of $G$ is a set $S$ of vertices of $G$ such that every vertex of $G$ is totally dominated by a vertex in $S$. The indicated…
We consider a simple game, the $k$-regular graph game, in which players take turns adding edges to an initially empty graph subject to the constraint that the degrees of vertices cannot exceed $k$. We show a sharp topological threshold for…
In order to find a causal explanation for data presented in the form of covariance and concentration matrices it is necessary to decide if the graph formed by such associations is a projection of a directed acyclic graph (dag). We show that…
We prove that Strings-and-Coins -- the combinatorial two-player game generalizing the dual of Dots-and-Boxes -- is strongly PSPACE-complete on multigraphs. This result improves the best previous result, NP-hardness, argued in Winning Ways.…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of two-player parity games over graphs of bounded tree-width, where updates may add or delete edges,…
Strategy improvement is a widely-used and well-studied class of algorithms for solving graph-based infinite games. These algorithms are parameterized by a switching rule, and one of the most natural rules is "all switches" which switches as…
The domination game is played on a graph $G$ by two players, named Dominator and Staller. They alternatively select vertices of $G$ such that each chosen vertex enlarges the set of vertices dominated before the move on it. Dominator's goal…
A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes…