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 …

A vertex coloring of a graph is said to be conflict-free with respect to neighborhoods if for
every non-isolated vertex there is a color appearing exactly once in its (open) neighborhood …

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 …

This paper is dedicated to studying the following question: Is it always possible to injectively
assign the weights 1,...,| E (G)| to the edges of any given graph G (with no component …

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 …

If S=(a1, a2,...) is a non-decreasing sequence of positive integers, then an S-packing
coloring of a graph G is a partition of V (G) into sets X1, X2,... such that for each pair of …

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 …

A\emph (k, t)-track layout of a graph G consists of a (proper) vertex t-colouring of G, a total
order of each vertex colour class, and a (non-proper) edge k-colouring such that between …