After a brief historical account, a few simple structural theorems about plane graphs useful
for coloring are stated, and two simple applications of discharging are given. Afterwards, the …

We introduce in this paper the notion of the chromatic number of an oriented graph G (that is
of an antisymmetric directed graph) defined as the minimum order of an oriented graph H …

The oriented chromatic number χo (G→) of an oriented graph G→=(V, A) is the minimum
number of vertices in an oriented graph H→ for which there exists a homomorphism of G→ …

The oriented chromatic number o (H) of an oriented graph H is defined as the minimum
order of an oriented graph H′ such that H has a homomorphism to H′. The oriented …

An oriented graph is a loopless digraph with no opposite arcs. An oriented k-colouring of an
oriented graph G ⃗ is a partition of its set of vertices into k parts in such a way that no two …

Abstract Let G_1=(V_1, E_1) and G_2=(V_2, E_2) be two edge-colored graphs (without
multiple edges or loops). A homomorphism is a mapping ϕ: V_1 ↦ V_2 for which, for every …

An oriented k-coloring of an oriented graph G (that is a digraph with no cycle of length 2) is a
partition of its vertex set into k subsets such that (i) no two adjacent vertices belong to the …

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 homomorphisms of oriented or undirected graphs, the oriented chromatic number, the
relationship between acyclic coloring number and oriented chromatic number, have been …

We combine two topics in directed graphs which have been studied separately, vertex
pushing and homomorphisms, by studying homomorphisms of equivalence classes of …