
An orientation of a graph \(H\) is a digraph obtained from \(H\) by giving to each edge one of its two possible orientations. A digraph \(G\) is an oriented graph if it is an orientation of some graph \(H\). An oriented \(k\)-coloring of an oriented graph \(G\) is a partition of the vertex set of \(G\) into \(k\) color classes such that no two adjacent vertices belong to the same color class and all the arcs linking two color classes have the same direction. The oriented chromatic number of an oriented graph \(G\) is the smallest \(k\) such that \(G\) has an oriented \(k\)-coloring. The oriented chromatic number of a graph \(H\) is the maximum of the oriented chromatic numbers of its orientations. This paper surveys the main results on oriented chromatic numbers.
oriented graph, oriented graph coloring, Directed graphs (digraphs), tournaments, directed graph, acyclic chromatic number, planar graphs, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science, Coloring of graphs and hypergraphs, graph homomorphism, Discrete Mathematics and Combinatorics
oriented graph, oriented graph coloring, Directed graphs (digraphs), tournaments, directed graph, acyclic chromatic number, planar graphs, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science, Coloring of graphs and hypergraphs, graph homomorphism, Discrete Mathematics and Combinatorics
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