关于扩张下保持的图等价
On graph equivalences preserved under extensions
摘要：
设R是图上的一个等价关系。R的加强是指关系R'使得图G和H在关系R'中，如果对任何图F，图G和F的并与图H和F的并在关系R中。本文研究了图的等价关系的加强问题。我们考虑的最重要的情况涉及由图属性定义的等价关系。我们得到了由k-连通图、k-可着色图、Hamilton图和平面图等性质决定的等价关系的加强结果。
英文摘要：
Let R be an equivalence relation on graphs. By the strengthening of R we mean the relation R' such that graphs G and H are in the relation R' if for every graph F, the union of the graphs G and F is in the relation R with the union of the graphs H and F. We study strengthenings of equivalence relations on graphs. The most important case that we consider concerns equivalence relations defined by graph properties. We obtain results on the strengthening of equivalence relations determined by the properties such as being a k-connected graph, k-colorable, hamiltonian and planar.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
