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 …

The clustered chromatic number of a graph class is the minimum integer $ t $ such that for
some $ C $ the vertices of every graph in the class can be colored in $ t $ colors so that …

An island in a graph is a set X of vertices such that each element of X has few neighbors
outside X. In this paper, we prove several bounds on the size of islands in large graphs …

We prove that every graph with circumference at most $ k $ is $ O (\log k) $-colourable such
that every monochromatic component has size at most $ O (k) $. The $ O (\log k) $ bound on …

For a positive integer $ g $, we study a family of plane graphs $ G $ without cycles of length
less than $ g $ that are maximal in a sense that adding any new edge to $ G $ either makes …

We study the problem of partitioning the vertex set of a given graph so that each part induces
a graph with components of bounded order; we are also interested in restricting these …

Given a graph G=(V, E) G=(V, E), an edge bipartization set of G is a subset E'⊆ E (G) E′⊆
E (G) such that G'=(V, E ∖ E') G′=(V, E\E′) is bipartite. An edge bipartization set that is …

Abstract In 1985, Mihok and recently Axenovich, Ueckerdt, and Weiner asked about the
minimum integer g∗> 3 such that every planar graph with girth at least g∗ admits a 2 …

A graph G has a (𝒫 k 1, 𝒫 k 2)-partition if V (G) can be partitioned into two nonempty disjoint
subsets V 1 and V 2 so that G [V 1] and G [V 2] are graphs whose components are paths of …

We study the problem of determining whether a given graph G=(V, E) admits a matching M
whose removal destroys all odd cycles of G (or equivalently whether GM is bipartite). This …