覆盖拟阵及其可图性

摘要

拟阵具有较强的公理系统，这为它和其他理论的结合奠定坚实的基础。文中利用覆盖构造一个拟阵，并研究这个拟阵的可图性。利用友元把论域的一个覆盖变成这个论域的一个划分，结合拟阵理论，建立这个覆盖的一个拟阵结构，并研究覆盖拟阵的极小圈与覆盖之间的关系。最后证明覆盖拟阵是一个可图拟阵。%Matroid theory has a powerful axiomatic system, which lays a solid foundation for the combination of matroids and other theories. A matroidal structure is constructed by a covering of a universe, and the graphical representation of the matroid is studied. Using the indiscernible neighborhoods, the partition of a universe is induced by a covering of the universe. Through the partition, the matroidal structure of the covering is constructed. The set of all circuits of the matroid is represented by the covering. Finally, the matroid is proved to be a graphic matroid.