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Consider the following probabilistic one-player game: The board is a graph with $n$ vertices, which initially contains no edges. In each step, a new edge is drawn uniformly at random from all non-edges and is presented to the player,…

Combinatorics · Mathematics 2009-11-20 Michael Belfrage , Torsten Mütze , Reto Spöhel

We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph. We say a player fills an edge if that player has picked all…

Discrete Mathematics · Computer Science 2026-04-14 Florian Galliot

The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…

Computational Complexity · Computer Science 2016-11-24 Carolin Albrecht , Frank Gurski , Jochen Rethmann , Eda Yilmaz

A set $S$ of vertices of a graph is a defensive alliance if, for each element of $S$, the majority of its neighbours is in $S$. We consider the notion of local minimality in this paper. We are interested in locally minimal defensive…

Computational Complexity · Computer Science 2023-03-06 Ajinkya Gaikwad , Soumen Maity , Shuvam Kant Tripathi

We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can…

Computational Complexity · Computer Science 2017-06-08 Till Fluschnik , Meike Hatzel , Steffen Härtlein , Hendrik Molter , Henning Seidler

We define a new escape game in graphs that we call Nemesis. The game is played on a graph having a subset of vertices labeled as exits and the goal of one of the two players, called the fugitive, is to reach one of these exit vertices. The…

Data Structures and Algorithms · Computer Science 2026-01-21 Pierre Bergé , Antoine Dailly , Yan Gerard

We show that Mis\`ere Partizan Arc Kayles is PSPACE-complete on planar graphs via a reduction from Bounded Two-Player Constraint Logic. Furthermore, we show how to embed our gadgets onto the square and triangular grids. In order to clearly…

Computational Complexity · Computer Science 2025-12-01 Kyle Burke , Caroline Cashman , Alfie Davies , Kanae Yoshiwatari , Francesca Yu

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

Computer Science and Game Theory · Computer Science 2026-04-20 Jonatha ANSELMI , Bruno Gaujal

The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in $NP \cap coNP$ which are not known to be in $P$. However, there are some…

Computational Complexity · Computer Science 2014-08-10 David Auger , Pierre COUCHENEY , Yann Strozecki

We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on…

Computer Science and Game Theory · Computer Science 2016-11-30 Sunil Simon , Dominik Wojtczak

We study the complexity of problems related to subgame-perfect equilibria (SPEs) in infinite duration non zero-sum multiplayer games played on finite graphs with parity objectives. We present new complexity results that close gaps in the…

Computer Science and Game Theory · Computer Science 2022-04-22 Léonard Brice , Marie van den Bogaard , Jean-François Raskin

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every…

Data Structures and Algorithms · Computer Science 2015-03-17 Dániel Marx , Igor Razgon

This work studies Stackelberg network interdiction games -- an important class of games in which a defender first allocates (randomized) defense resources to a set of critical nodes on a graph while an adversary chooses its path to attack…

Optimization and Control · Mathematics 2023-01-31 Tien Mai , Avinandan Bose , Arunesh Sinha , Thanh H. Nguyen

Broadcast networks allow one to model networks of identical nodes communicating through message broadcasts. Their parameterized verification aims at proving a property holds for any number of nodes, under any communication topology, and on…

Logic in Computer Science · Computer Science 2023-06-22 Nathalie Bertrand , Patricia Bouyer , Anirban Majumdar

We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity…

Computational Complexity · Computer Science 2015-12-12 Matthias Mnich , Heiko Röglin , Clemens Rösner

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions S and T of size k, whether it is…

Computational Complexity · Computer Science 2015-02-18 Daniel Lokshtanov , Amer E. Mouawad , Fahad Panolan , M. S. Ramanujan , Saket Saurabh

A set S of vertices of a graph is a defensive alliance if, for each element of S, the majority of its neighbors is in S. The problem of finding a defensive alliance of minimum size in a given graph is NP-hard and there are polynomial-time…

Computational Complexity · Computer Science 2017-07-17 Bernhard Bliem , Stefan Woltran

Hedonic games model settings in which a set of agents have to be partitioned into groups which we call coalitions. In the enemy aversion model, each agent has friends and enemies, and an agent prefers to be in a coalition with as few…

Computer Science and Game Theory · Computer Science 2025-02-20 Martin Durand , Laurin Erlacher , Johanne Müller Vistisen , Sofia Simola

We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the…

Formal Languages and Automata Theory · Computer Science 2020-02-19 Dhananjay Raju , Rüdiger Ehlers , Ufuk Topcu

We investigate the combinatorial game Slime Trail.This game is played on a graph with a starting piece in a node. Each player's objective is to reach one of their own goal nodes. Every turn the current player moves the piece and deletes the…

Computational Complexity · Computer Science 2017-12-14 Matthew Ferland , Kyle Burke