New 4-Color Algorithm And Its Application

Four-color problem is the core issue in the field of graph theory. The proof of Four-color theorem means that all the theorem equivalent to Four-color theorem be proved, such as Kaufman's cross product conjecture and the solution existence of the Diophantine Equations conjecture which have thousands of parameters established by Matiyasevich at the same time. The proof of four-color theorem shows the truth of its equivalence problem from other areas. It can explain the isomorphism ideology of graph theory in other areas. Therefore, this research has a certain value.The main conclusion reads as follows:Firstly, we introduce the nature of the four-color problem, analyze the proofs for four-color theorem of several different ideas and a variety of methods, and point out the advantages and disadvantages. Then explain the link between four-color theorem and its algorithm.Secondly, we research vertex-coloring theory and vertex-coloring algorithm based on vertex-coloring theory, introduce Kempe's four-color theory and Kempe-Kittel algorithm based on Kempe theorem, analyze the disadvantages as well as defects in the algorithm, and give a improved algorithm based on it. At last, we offer some examples to explain how the improved algorithm work for avoiding irrevocable Kemp tangle to verify its effectiveness.Thirdly, we research the edge coloring theory and four-color algorithm based on edge coloring, analyze Tait's edge coloring theory and its drawbacks, then try to combine the theory of Kempe with Tait's edge coloring theory, and try to prove four-color theorem by applying bipartite graph theory and matching theory. Finally, we discuss the value of the proof of four-coloring problem and its algorithm in academic fields and practical application fields, and then make a prospect of the development of four-color theorem.