Consider the following two ways to colour the vertices of a graph where the requirement that
adjacent vertices get distinct colours is relaxed. A colouring has" defect" $ d $ if each …

Complexity theory is built fundamentally on the notion of efficient reduction among
computational problems. Classical reductions involve gadgets that map solution fragments …

Graph theory, a branch of mathematics, studies the relationships between entities using
vertices and edges. Uncertain Graph Theory has emerged within this field to model the …

We study deterministic, distributed algorithms for two weak variants of the standard graph
coloring problem. We consider defective colorings, ie, colorings where nodes of a color …

A graph G is m-choosable with impropriety d, or simply (m, d)*-choosable, if for every list
assignment L, where [mid] L (v)[mid][ges] m for every v∈ V (G), there exists an L-colouring of …

Hadwiger's conjecture asserts that every K t‐minor‐free graph has a proper (t− 1)‐colouring.
We relax the conclusion in Hadwiger's conjecture via improper colourings. We prove that …

Given a simple undirected graph, the problem of finding a maximum subset of vertices
satisfying a nontrivial, interesting property Π that is hereditary on induced subgraphs, is …

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 …

Archdeacon (1987) proved that graphs embeddable on a fixed surface can be 3-coloured so
that each colour class induces a subgraph of bounded maximum degree. Edwards, Kang …

Hadwiger's conjecture asserts that if a simple graph G has no K_t+1 minor, then its vertex set
V(G) can be partitioned into t stable sets. This is still open, but we prove under the same …