If a graph has bounded clique number and sufficiently large chromatic number, what can we
say about its induced subgraphs? András Gyárfás made a number of challenging …

The celebrated Kővári-Sós-Turán theorem states that any n-vertex graph containing no copy
of the complete bipartite graph K s, s has at most O s (n 2− 1/s) edges. In the past two …

In 1960, Asplund and Grünbaum proved that every intersection graph of axis-parallel
rectangles in the plane admits an O (ω 2)-coloring, where ω is the maximum size of a clique …

We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rz\k {a}\. zewski, Thomass\'e, and
Walczak, that for every graph $ H $, there is a polynomial $ p $ such that for every positive …

In this paper we prove that for every $ s\geq 2$ and every graph $ H $ the following holds.
Let $ G $ be a graph with average degree $\Omega_H (s^{C| H|^ 2}) $, for some absolute …

This thesis contains a brief overview of my research activities between 2009 and 2017 as
Chargé de Recherche CNRS at the G-SCOP laboratory in Grenoble, France. I chose to …

An intersection graph of curves in the plane is called a string graph. Matoušek almost
completely settled a conjecture of the authors by showing that every string graph with m …

We prove that if $\mathcal {C} $ is a hereditary class of graphs that is polynomially $\chi $-
bounded, then the class of graphs that admit decompositions into pieces belonging to …

Treewidth is an important graph invariant, relevant for both structural and algorithmic
reasons. A necessary condition for a graph class to have bounded treewidth is the absence …

We prove a decomposition theorem for graphs that do not contain a subdivision of K4 as an
induced subgraph where K4 is the complete graph on four vertices. We obtain also a …