 
Summary: Graph Theory Worksheet Math 105, Fall 2010 Page 1
Graph Colorings
Definition: A (vertex) coloring of a graph is an assignment of colors to the vertices of the
graph so that vertices that are joined by an edge (adjacent vertices) have different colors.
Example:
Definition: For a graph G, the smallest number of colors needed to color G is called
the chromatic number of G and is denoted (G). Note that is the Greek letter chi, for
chromatic.
Example: If G is , then (G) = 3. It is possible to color G using just 3
colors, and we need at least 3 colors because G has a triangle.
Example: If G is find (G).
Graph Theory Worksheet Math 105, Fall 2010 Page 2
1. Color each of the vertices of the following graph red (R), white (W), or blue (B) in
such a way that no adjacent vertices have the same color.
2. What is the coloring number of the following complete graphs?
Ki (Ki)
K1 =
K2 =
K3 =
K4 =
