我所初识的高等图论(Ⅳ):二重图上Euler回

Advanced Graphs Theory as I have Initially Realized(Ⅳ) :Euler Tours on Double Graphs

系统地介绍了作者早期在图的上可嵌入性和最大亏格方面所进行的开创性的工作.然后把二重图、标准Euler回、叉帽与手柄、上可嵌入性与最大亏格等归结为,由他所成形的多面形理论体系.在此基础上,特别反映了国内在这一领域的独特研究进展,包括理论层面和实际应用层面.

This paper gives a systematic survey based on the author＇s own pioneering work on the up - embed-dability and maximum genus of graphs. Then, double graphs, standard Euler tour, the crosscaps and handles, up- embeddability and maximum genus etc are integrated into his polyhedral theory system. On this basis, the particular research progress including theoretical basis and practical applications in this field at our country are briefly reviewed.