Let I(G) denote the set of all independent sets of vertices of a graph G, and let I(G, u) denote the independent sets of G that contain the vertex u. A fractional coloring of G is then a nonnegative real function f on I(G) such that for any vertex u of G, sum_(S element I(G, u)) f(S)>=1. The sum of values of f is called its weight, and the minimum possible weight of a fractional coloring is called the fractional chromatic number χ^*(G).

chromatic number | fractional chromatic number | minimum vertex coloring | vertex coloring