56 citations · 270 across the 25 of their papers we have counts for
8 papers · 1 filter
Parameterized algorithm for weighted independent set problem in bull-free graphs
Stéphan Thomassé, Nicolas Trotignon, Kristina Vusković
The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding if a bull-free graph…
Linear balanceable and subcubic balanceable graphs
Pierre Aboulker, Marko Radovanović, Nicolas Trotignon +2
In [{Structural properties and decomposition of linear balanced matrices}, {\it Mathematical Programming}, 55:129--168, 1992], Conforti and Rao conjectured that every balanced bipa…
Graphs that do not contain a cycle with a node that has at least two neighbors on it
Pierre Aboulker, Marko Radovanović, Nicolas Trotignon +1
We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected…
Combinatorial optimization with 2-joins
Nicolas Trotignon, Kristina Vušković
A 2-join is an edge cutset that naturally appears in decomposition of several classes of graphs closed under taking induced subgraphs, such as perfect graphs and claw-free graphs.…
On Roussel-Rubio-type lemmas and their consequences
Nicolas Trotignon, Kristina Vušković
Roussel and Rubio proved a lemma which is essential in the proof of the Strong Perfect Graph Theorem. We give a new short proof of the main case of this lemma. In this note, we als…
A structure theorem for graphs with no cycle with a unique chord and its consequences
Nicolas Trotignon, Kristina Vušković
We give a structural description of the class of graphs that do not contain a cycle with a unique chord as an induced subgraph. Our main theorem states that any connected…
Algorithms for square--free Berge graphs
Frédéric Maffray, Nicolas Trotignon, Kristina Vušković
We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths induce a ho…
Coloring perfect graphs with no balanced skew-partitions
Maria Chudnovsky, Nicolas Trotignon, Théophile Trunck +1
We present an algorithm that computes a maximum stable set of any perfect graph with no balanced skew-partition. We present time algorithm that colors them.