探索Euler图的等价命题

Exploring equivalent definitions of eulerian graphs

从研究Euler图的等价命题入手,尝试挖掘Euler图的拓扑结构,力图从多个角度刻画Euler图的本征,得到4个新的Euler图等价命题,并利用图的"浓缩"和"稀释"运算给出刻画Euler图的技术,且此技术能够转化为可行的算法.

From the topic of equivalent propositions of eulerian graph to start our study, we try to dig the topology of eulerian graph, and to describe eulerian graph from the view of different insights. Finally, we obtain four new equivalent propositions of eulerian graph by the technique of “concentration” and “dilution” operations, which can be transformed into two feasible algorithms.