A Research On Berge's Thought Of Graph Theory

Graph theory is an important branch of mathematics.It has been more than 300 years old.After the computer-assisted proof of the four-color theorem in the 1970 s,there is another important achievement in graph theory early in this century,which is the proof of the strong perfect graph theorem.As the pioneer of modern graph theory,French mathematician Claude Berge is not only the proponent of the perfect graph conjecture,but also provides a breakthrough for the final proof of the theorems.Berge's thought has an important influence on many aspects of graph theory.So far,relevant researches at home and abroad are few and not systematic.According to the chronological order and Berge's thoughts,this dissertation tries to summarize and study Berge's contributions and significant influences,and in the process of which the comparative methods and literature analysis play an important role.The main results are as follows:1.This dissertation reviews Berge's life.It studies the reasons why Berge entered the field of graph theory,and how to promote the rapid development of graph theory,which reveals the important position of Berge in graph theory.2.This dissertation summarizes the background of Berge's initial graph theory.Comparing K?nig's thoughts and works with Berge's,it points out that Berge attaches importance not only to theory but also to the application of graph theory in other disciplines.3.This dissertation studies Berge's two pioneering contributions,perfect graph theory and hypergraph theory.Taking the development of perfect graph as the main line,it expounds the origin of the perfect graph,and the history of the proof of strong and weak perfect theorems.This focus on how Berge's hypergraph thought and decomposition method result in the final proof of theorems,then explores the further development of perfect graph theory.4.This dissertation analyzes the influence of Berge's thought on the successors.In addition to studying Berge's students are deeply influenced by his thoughts,it focu-ses on how Berge affects Chvátal's interest in research.