Some Results on Fractional Graph Theory

We will convert integer-based definitions and invariants into their fractional analogues. Some results on fractional factors, fractional Hamiltonian graphs, fractional (g, f)-factors and fractional colorings are presented. The relationships of the programming and the graph theory are discussed. In particular, some new results related to fractional (g, f)-factors obtained by us are given. Furthermore, some open problems are presented.