Coloring of the graphs

Anna Powolny

Graph Coloring?

• Special case of graph labeling
• Assignment of labels - colors - to elements of a graph

Vertex Coloring

Vertex Coloring

• no two vertices sharing the same edge have the same color.
• Graphs are loopless. (connection never directly back to itself)

k-coloring

- coloring using at most k colors

k-colorable 

- graph having k-coloring (chromatic number χ(G)<=k)

chromatic number

- χ(G) - the smallest number of colors needed to color a graph. G.

k-chromatic graph

- chromatic number χ(G) = k