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In graph theory, oriented graph coloring is a special type of graph coloring. Namely, it isan assignment of colors to vertices of an oriented graph that
Equivalently, an oriented graph coloring of a graph G is an oriented graph H such that there exists a homomorphism from G to H.
An oriented chromatic number of a graph G is the fewest colors needed in an oriented coloring;it is usually denoted by χ o {\displaystyle \scriptstyle \chi _{o}}. The same definition can be extended to undirected graphs, as well, by defining the oriented chromatic number of an undirected graph to be the largest oriented chromatic number of any of its orientations.
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