Lesson plan
Oriented coloring
s can be 2-colored, this oriented bipartite graph requires at least 3 colors, meaning its oriented chromatic number \chi_o(G) = 3 . In graph theory, oriented graph coloring is a special type of graph coloring. Namely, it is an assignment of colors to vertices of an oriented graph that * is proper: no two adjacent vertices get the same color, and * is consistently oriented: for each two edges connecting vertices of the same two colors, both edges have the same color at their start and the same color at their destination. Here, an oriented graph is a special kind of directed graph, with at most one directed edge between each pair of vertices. An oriented graph coloring of a graph G can be described equivalently as another oriented graph H whose vertices represent colors, together with a homomorphism from G to H . The homomorphism maps each vertex in G to its color in H . The oriented chromatic number of an oriented graph G is the fewest colors needed in an oriented coloring; it is usually denoted by \chi_o(G) . 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.
Article summary
s can be 2-colored, this oriented bipartite graph requires at least 3 colors, meaning its oriented chromatic number \chi_o(G) = 3 . In graph theory, oriented graph coloring is a special type of graph coloring. Namely, it is an assignment of colors to vertices of an oriented graph that * is proper: no two adjacent vertices get the same color, and * is consistently oriented: for each two edges connecting vertices of the same two colors, both edges have the same color at their start and the same color at their destination. Here, an oriented graph is a special kind of directed graph, with at most one directed edge between each pair of vertices. An oriented graph coloring of a graph G can be described equivalently as another oriented graph H whose vertices represent colors, together with a homomorphism from G to H . The homomorphism maps each vertex in G to its color in H . The oriented chromatic number of an oriented graph G is the fewest colors needed in an oriented coloring; it is usually denoted by \chi_o(G) . 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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