欧拉子式与4-正则平面图的简洁递归刻画
Eulerian-minors and a concise recursive characterization of 4-regular planar graphs
AI总结：
本文利用欧拉子式关系刻画欧拉图、平面欧拉图和外平面欧拉图，并给出4-正则平面图的简洁递归刻画。
摘要：
欧拉图的欧拉子式是通过收缩该欧拉图的欧拉子图而得到的。欧拉子式运算保持图的欧拉性质，并且欧拉图在欧拉子式关系下是良拟序的。本文通过排除欧拉子式来刻画欧拉图、平面欧拉图和外平面欧拉图，并对4-正则平面图给出了简洁的递归刻画。
英文摘要：
An Eulerian-minor of an Eulerian graph is obtained from an Eulerian subgraph of the Eulerian graph by contraction. The Eulerian-minor operation preserves Eulerian properties of graphs and moreover Eulerian graphs are well-quasi-ordered under Eulerian-minor relation. In this paper, we characterize Eulerian, planar and outer-planar Eulerian graphs by means of excluded Eulerian-minors, and provide a concise recursive characterization to 4-regular planar graphs.
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