Graph Theory and topology , graph theory and algebraic case studies of cross-cutting issues
|Keywords||Polyhedron formula Euler - Poincaré characteristic number Guthrie problem Hadwiger conjecture Wagner theorem Thumbnail ( graph minor ) Loop base set Polya enumeration theorem|
Within the Mathematical Sciences, ideas and methods between different disciplines branch cross each other, mutual penetration is one of the important trends in the development of Mathematical Sciences; This paper focuses on the central idea, selected graph theory and topology, graph theory and algebraic cross-cutting issues as case, try some typical questions for case studies, from the perspective of the history of the concept of development, the timing analysis for each question, follow the ideological interpretation of the law to explore this cross-integration of the development to a certain extent will lead to major discoveries, or even cross-disciplinary produce; pointed out that cross-cutting issues of historical research to elucidate the mathematical law of development of special significance; author believes that by the mathematical internal factors - cross-cutting issues to analyze the development of the power of mathematics, history of mathematics in a new Analysis of the direction. On the specific content, the text is divided into four parts, the first part from the polyhedron formula to Euler - Poincaré characteristic number, investigated how this process is beyond the concept of measure, and how towards the topology development; section describes Hadwiger conjecture from Guthrie problem to ideological evolution, examines the coloring of the two development path; On the one hand due to the consideration of characteristics of surface topology, resulting in the formation of the chromatic number theory, plays an important milestone in the development of topological graph theory significance; Wagner's theorem on the other hand analysis of the key factors to trigger Hadwiger made his famous conjecture, pointed out that the introduction of the \. These two parts are graph theory and topology examples of cross-cutting issues; algebraic thinking of the third section describes the circuit of the the loop base set structure, the deepening of the process of algebraic tools and algebraic methods, and how this process prompted Whitby The Nigerian first introduced matroid (1935). Described at the beginning of the fourth part from the simplest figure - tree and its early count until the the Polya count theorem proposed, which is linked to the idea of ??a permutation group theory, to further study the cross thinking it contains a good start! loop algebra and the development of the theory of tree count two classic problems on graph theory and algebra. On the whole, the four parts together, discussed the evolution trend of Mathematical Sciences internal disciplinary infiltrated, investigated the historical background and development process of these cross-cutting issues also reflects an important aspect of mathematical unity, a deep understanding of modern mathematics cross penetrate the trend is of great value.