The Research On The Fractional Chromatic Number Of Graphs

The coloring of graphs is an important domain in the graph theory, Hedetniemi' conjecture has not been resolved; the fractional coloring of graphs is a natural generalization of the coloring of graphs. The fractional coloring of products and expansion graph is discussed in this paper. The fractional chromatic number of products, which is vertex transitive and connected, is determined in this paper. And this is true for Hedetnimi' conjecture on the fractional coloring. Then the fractional chromatic number of expansion graph of products is researched, and it is an application to the expansion graph.