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Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, corresponding problems in graphs are also transformed into ones in covering-based rough sets. For example, finding a minimal edge cover of a graph is translated into finding a minimal general reduct of a covering. The main contributions of this paper are threefold. First, any graph is converted to a covering. Two graphs induce the same covering if and only if they are isomorphic. Second, some new concepts are defined in covering-based rough sets to correspond with ones in graph theory. The upper approximation number is essential to describe these concepts. Finally, from a new viewpoint of covering-based rough sets, the general reduct is defined, and its equivalent characterization for the edge cover is presented. These results show the potential for the connection between covering-based rough sets and graphs.<\/jats:p>","DOI":"10.1155\/2013\/519173","type":"journal-article","created":{"date-parts":[[2013,5,22]],"date-time":"2013-05-22T21:29:08Z","timestamp":1369258148000},"page":"1-7","source":"Crossref","is-referenced-by-count":4,"title":["Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets"],"prefix":"10.1155","volume":"2013","author":[{"given":"Shiping","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingxin","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, 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