The Early History Of Topological Graph Theory

Topological graph theory is an important part of modern mathematics.It is a new subject with rapid development and wide application in the 20 th century.As an interdisciplinary subject between graph theory and topology,its core content is to study the problems of embedding graphs on surfaces.This dissertation hackles the early historical development of topological graph theory before it formally become an independent subject.The development of map coloring to the theory of graph embedding surfaces is explored step by step,and the significance of the work of Kuratowski,Whitney,Ringle and Youngs in promoting the development of topological graph theory is analyzed.The origin and preliminary establishment of topological graph theory are analyzed and studied in a comprehensive and systematic way through the literature analysis and comparison.The main results are as follows:1.The dissertation investigates the problems of early topological graph theory,points out the first problem in topological graph theory is the seven bridges in K?nigsberg,discusses the topological properties of Euler polyhedron formula,analyzes the four-color theorem and the Heawood conjecture how to promote the research of graphs embedding on surfaces.2.The dissertation analyzes the development from map coloring to graphs embedded surfaces.Through expounding the work of Kuratowski,Whitney,MacLane and Tutte on the theory of planar graph,the profound ideas contained in the theory of planar graph are studied,and the important position of the theory of planar graph in topological graph theory is revealed.Through hackling the progress of Heawood conjecture for 78 years,the importance of the combination methods contained in Ringle-Youngs in solving the problems of graphs embedding surfaces is revealed,and the significance of complete graph theorem to the establishment of topological graph theory is analyzed.3.The dissertation contrasts the two books of Graphs,Groups and Surfaces and Topological Graph Theory,which marks the establishment of topological graph theory.It is pointed out that Graphs,Groups and Surfaces is the first book that contains the main contents of the early topological graph theory,and Topological Graph Theory is the first book namedafter topological graph theory for the first time.