A vertex coloring f of a graph G is nonrepetitive if there are no integer r≥ 1 and a simple
path v1,…, v2r in G such that f (vi)= f (vr+ i) for all i= 1,…, r. This notion is a graph‐theoretic …

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 …

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 …

Acyclic, Star and Oriented Colourings of Graph Subdivisions Page 1 Discrete Mathematics
and Theoretical Computer Science 7, 2005, 37–50 Acyclic, Star and Oriented Colourings of …

This chapter is a survey of the four standard associative digraph products, namely the
Cartesian, strong, direct and lexicographic products. Topics include metric properties …

In this paper, we study homomorphisms of 2-edge-colored graphs, that is graphs with edges
colored with two colors. We consider various graph classes (outerplanar graphs, partial 2 …

We examine subgraphs of oriented graphs in the context of oriented coloring that are
analogous to cliques in traditional vertex coloring. Bounds on the sizes of these subgraphs …

In this paper we consider directed cographs, which are defined by Bechet et al. by the
disjoint union, series, and order composition, from an algorithmic point of view. Using their …

The clique number of an undirected graph G is the maximum order of a complete subgraph
of G and is a well‐known lower bound for the chromatic number of G. Every proper k …

An oriented graph is a directed graph with no cycle of length at most two. A homomorphism
of an oriented graph to another oriented graph is an arc preserving vertex mapping. To push …