An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that every oriented graph with maximum average degree strictly less than 10 3 has an oriented chromatic number at most 16. This implies that every oriented planar graph with girth at least 5 has an oriented chromatic number at most 16, that improves the previous known bound of 19 d...

An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that every oriented graph with maximum average degree less than 10 3 has an oriented chromatic number at most 16. This implies that every oriented planar graph with girth at least five has an oriented chromatic number at most 16, that improves the previous known bound of 19 due to ...

Oriented chromatic number of an oriented graph G is the minimum order of an oriented graph H such that G admits a homomorphism to H . The oriented chromatic number of an unoriented graph G is the maximal chromatic number over all possible orientations of G. In this paper, we prove that every Halin graph has oriented chromatic number at most 8, improving a previous bound by Hosseini Dolama and S...

A homomorphism from an oriented graph G to an oriented graph H is a mapping φ from the set of vertices of G to the set of vertices of H such that −−−−−→ φ(u)φ(v) is an arc in H whenever −→uv is an arc in G. The oriented chromatic index of an oriented graph G is the minimum number of vertices in an oriented graph H such that there exists a homomorphism from the line digraph LD(G) of G to H (Reca...

To push a vertex v of a directed graph −→ G is to change the orientations of all the arcs incident with v. An oriented graph is a directed graph without any cycle of length at most 2. An oriented clique is an oriented graph whose non-adjacent vertices are connected by a directed 2-path. A push clique is an oriented clique that remains an oriented clique even if one pushes any set of vertices of...

The oriented chromatic number of an oriented graph −→ G is the minimum order of an oriented graph −→ H such that −→ G admits a homomorphism to −→ H . The oriented chromatic number of an undirected graph G is then the greatest oriented chromatic number of its orientations. In this paper, we introduce the new notion of the upper oriented chromatic number of an undirected graph G, defined as the m...