Abstract 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.
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2014, Vol. 27 
