## Research topics

My research topics are mainly focused on homomorphisms and graph colorings, vertex partitions, discharging methods, entropy compression method, and recently on combinatorics on words.

*Homomorphisms and graph colorings*

I’m interested in the*oriented coloring*of graphs. The notion of homomorphism is closely related to the notion of graph coloring, and therefore a part of my work consists to prove that, for a given graph class , every graph of admits a homomorphism to a given tournament.The*Discharging method*

*discharging method*is one of the famous methods used to prove that a planar graph or a graph with bounded maximum average degree admits a given coloring. I am interested in this notion and its improved version, that is the*global*discharging method where the weight can travel arbitrarily far away from the source.

The Four Color Theorem says that the vertices of a planar graph can be partitioned into four empty graphs. I have particular interest in the following question: What happens if we want to partition the vertices into classes such as paths, forests, graphs with maximum degree at most , graphs with order at most ? It is for example known that the vertices of a planar graph can be partitioned into three linear forests, or into a forest and a forest of maximum degree at most 5.*Vertex partitions of planar graphs*

The*Entropy compression method*

*entropy compression method*is a method derived from a breakthrough by Moser and Tardos who provide algorithmic version of the Lovász Local Lemma in quite general circumstances. This nice method seems to be applicable to colorings problems whenever the Local Lovasz Lemma is, with the benefits of providing tighter bounds.I recently became interested in problems of combinatorics on words such as pattern avoidance, repetition threshold, or generalization of Thue sequences.*Combinatorics on words*

## Projects

2017 - 2021 | ANR Project HOSIGRA (HOmomorphisms of SIgned GRAphs) |

2014 - 2016 | PHC Proteus Project with Ljubljana University, Slovenia (Coloring graphs on surfaces) |

2012 - 2015 | ANR Project EGOS (Embedded Graphs and their Oriented Structures) |

2012 - 2014 | PEPS Project HOGRASI (Homomorphism of signed graphs) |

2009 - 2012 | ANR Project GRATOS (GRAphs through TOpological Structure) |

## PhD student

2015 - ... | François Dross, La conjecture de Albertson et Berman (1976) et ses variations. (co-supervision with M. Montassier) |

2011 - 2015 | Marthe Bonamy, Global discharging procedures to settle graph optimisation problems (co-supervision with B. Lévêque) |

## GDR-IM

From 2012 to 2016, I was co-head of the GT Graphes, workshop of the GDR Informatique Mathématique of CNRS.