Fractional coloring

Fractional coloring is a concept in graph theory that generalizes the notion of graph coloring. In classical graph coloring, each vertex of a graph is assigned a color such that no two adjacent vertices share the same color. The objective is often to minimize the number of colors used, which is known as the chromatic number of the graph. In fractional coloring, instead of assigning whole colors to vertices, a "fractional color" can be assigned to a vertex using a weight or a fractional representation.