We give a very simple proof that every non-bipartite matching covered graph contains a nice subgraph that is an odd subdivision of K-4 or (C) over bar(6). Tt follows immediately that every brick different From K-4 and (C) over bar(6) has an edge whose removal preserves the matching covered property. These are classical and very useful results due to Lovasz. (C) 1996 Academic Press, Inc. [References: 7]
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