Category:Definitions/Graph Colorings

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This category contains definitions related to Graph Colorings.
Related results can be found in Category:Graph Colorings.


Vertex Coloring

A vertex $k$-coloring of a simple graph $G = \left({V, E}\right)$ is defined as an assignment of one element from a set $C$ of $k$ colors to each vertex in $V$.

That is, a vertex $k$-coloring of the graph $G = \left({V, E}\right)$ is a mapping $c: V \to \left\{{1, 2, \ldots k}\right\}$.


A graph with such a coloring is called a vertex-colored graph.


Edge Coloring

An edge $k$-coloring of a simple graph $G = \left({V, E}\right)$ is defined as an assignment of one element from a set $C$ of $k$ colors to each edge in $E$.

That is, an edge $k$-coloring of the graph $G = \left({V, E}\right)$ is a mapping $c: E \to \left\{{1, 2, \ldots k}\right\}$.


A graph with such a coloring is called an edge-colored graph.

Pages in category "Definitions/Graph Colorings"

The following 6 pages are in this category, out of 6 total.