9 citations · 11 across the 17 of their papers we have counts for
22 papers
A two-player version of the assignment problem
Florian Galliot, Nacim Oijid, Jonas Sénizergues
We introduce the competitive assignment problem, a two-player version of the well-known assignment problem. Given a set of tasks and a set of agents with different efficiencies for…
On the Complexity of Vertex-Splitting Into an Interval Graph
Faisal N. Abu-Khzam, Dipayan Chakraborty, Lucas Isenmann +1
Vertex splitting is a graph modification operation in which a vertex is replaced by multiple vertices such that the union of their neighborhoods equals the neighborhood of the orig…
An Algorithm for Monitoring Edge-geodetic Sets in Chordal Graphs
Clara Marcille, Nacim Oijid
A monitoring edge-geodetic set (or meg-set for short) of a graph is a set of vertices such that if any edge is removed, then the distance between some two vertices of incre…
Token positional games
Guillaume Bagan, Quentin Deschamps, Florian Galliot +2
The classical Maker-Breaker positional game is played on a board which is a hypergraph , with two players, Maker and Breaker, alternately claiming vertices of $\mathca…
On the parameterized complexity of the Maker-Breaker domination game
Guillaume Bagan, Mathieu Hilaire, Nacim Oijid +1
Since its introduction as a Maker-Breaker positional game by Duchêne et al. in 2020, the Maker-Breaker domination game has become one of the most studied positional games on vertic…
On the complexity of the Maker-Breaker happy vertex game
Mathieu Hilaire, Perig Montfort, Nacim Oijid
Given a c-colored graph G, a vertex of G is happy if it has the same color as all its neighbors. The notion of happy vertices was introduced by Zhang and Li to compute the homophil…
Exact number of flips required to sort a burnt stack of pancakes
Gerold Jäger, Nacim Oijid
In this work, we consider the burnt pancake problem, which is a well-studied problem going back to a work of Gates and Papadimitriou from 1979.The problem is to sort a stack of~…
Graph Irregularity via Edge Deletions
Julien Bensmail, Noémie Catherinot, Foivos Fioravantes +2
We pursue the study of edge-irregulators of graphs, which were recently introduced in [Fioravantes et al. Parametrised Distance to Local Irregularity. IPEC, 2024]. That is, we are…
Bounded degree QBF and positional games
Nacim Oijid
The study of SAT and its variants has provided numerous NP-complete problems, from which most NP-hardness results were derived. Due to the NP-hardness of SAT, adding constraints to…
Computing the degreewidth of a digraph is hard
Pierre Aboulker, Nacim Oijid, Robin Petit +2
Given a digraph, an ordering of its vertices defines a backedge graph, namely the undirected graph whose edges correspond to the arcs pointing backwards with respect to the order.…
On the complexity of Client-Waiter and Waiter-Client games
Valentin Gledel, Nacim Oijid, Sébastien Tavenas +1
Positional games were introduced by Hales and Jewett in 1963, and their study became more popular after Erdos and Selfridge's first result on their connection to Ramsey theory and…
Poset Positional Games
Guillaume Bagan, Eric Duchêne, Florian Galliot +5
We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset…
Complexity and algorithms for Arc-Kayles and Non-Disconnecting Arc-Kayles
Kyle Burke, Antoine Dailly, Nacim Oijid
Arc-Kayles is a game where two players alternate removing two adjacent vertices until no move is left, the winner being the player who played the last move. Introduced in 1978, its…
The Maker-Breaker Largest Connected Subgraph Game
Julien Bensmail, Foivos Fioravantes, Fionn Mc Inerney +2
Given a graph and , we introduce the following game played in . Each round, Alice colours an uncoloured vertex of red, and then Bob colours one blue (i…
Fast winning strategies for the attacker in eternal domination
Guillaume Bagan, Nicolas Bousquet, Nacim Oijid +1
Dominating sets in graphs are often used to model some monitoring of the graph: guards are posted on the vertices of the dominating set, and they can thus react to attacks occurrin…
The Maker-Maker domination game in forests
Eric Duchêne, Arthur Dumas, Nacim Oijid +2
We study the Maker-Maker version of the domination game introduced in 2018 by Duchêne et al. Given a graph, two players alternately claim vertices. The first player to claim a domi…
On the Parameterized Complexity of Relaxations of Clique
Ambroise Baril, Antoine Castillon, Nacim Oijid
We investigate the parameterized complexity of several problems formalizing cluster identification in graphs. In other words we ask whether a graph contains a large enough and suff…
Complexity of Maker-Breaker Games on Edge Sets of Graphs
Eric Duchêne, Valentin Gledel, Fionn Mc Inerney +4
We study the algorithmic complexity of Maker-Breaker games played on the edge sets of general graphs. We mainly consider the perfect matching game and the -game. Maker wins if s…
Incidence, a Scoring Positional Game on Graphs
Guillaume Bagan, Quentin Deschamps, Eric Duchêne +5
Positional games have been introduced by Hales and Jewett in 1963 and have been extensively investigated in the literature since then. These games are played on a hypergraph where…
Avoidance games are PSPACE-Complete
Valentin Gledel, Nacim Oijid
Avoidance games are games in which two players claim vertices of a hypergraph and try to avoid some structures. These games are studied since the introduction of the game of SIM in…
Bipartite instances of INFLUENCE
Eric Duchêne, Nacim Oijid, Aline Parreau
The game INFLUENCE is a scoring combinatorial game that has been introduced in 2020 by Duchene et al. It is a good representative of Milnor's universe of scoring games, i.e. games…
Generalising the achromatic number to Zaslavsky's colourings of signed graphs
Julien Bensmail, François Dross, Nacim Oijid +1
The chromatic number, which refers to the minimum number of colours required to colour the vertices of graphs properly, is one of the most central notions of the graph chromatic th…