From the 1 of 7 linked papers with an AI index.
7 papers
Acyclic Dichromatic Number of Tournaments: these are the Champions
Pierre Aboulker, Pierre Charbit, Samuel Coulomb +2
The paper characterizes the subtournaments that must occur in any tournament with a sufficiently large acyclic dichromatic number, confirming a conjecture and establishing a local‑…
Clique number of tournaments
Pierre Aboulker, Guillaume Aubian, Pierre Charbit +1
Given a digraph together with an ordering of its vertices, the \emph{backedge graph} of with respect to is the undirected graph with the same ve…
Decomposing tournaments into comparability graphs
Pierre Aboulker, Logan Crew, Julien Duron +7
In this note, we introduce the \emph{partial order decomposition number} of a digraph , denoted , defined as the minimum integer such that $A(D)=A(P_1)\cup\cdots\cup…
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.…
Finding forest-orderings of tournaments is NP-complete
Pierre Aboulker, Guillaume Aubian, Raul Lopes
Given a class of (undirected) graphs , we say that a Feedback Arc Set (FAS for short) is a -FAS if the graph induced by the edges of (forgetting t…
Induced Disjoint Paths Without an Induced Minor
Pierre Aboulker, Ãdouard Bonnet, Timothé Picavet +1
We exhibit a new obstacle to the nascent algorithmic theory for classes excluding an induced minor. We indeed show that on the class of string graphs -- which avoids the 1-subdivis…