Kuratowski's and Wagner's Theorems for Matroids.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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In an earlier paper the author proved the following theorem which provides a strengthening of Tuttes well-known characterization of regular totally unimodular matroids A binary matroid is regular if it does not have the Fano matroid or its dual as a series-minor parellel-minor. In this paper the author proves two theorems which provide the same kind of strengthening for Tuttes characterization of the graphic matroids i.e., bond-matroids. These two theorems are called Kuratowskis and Wagners Theorems for Matroids in view of the graph theoretic results which they generalize.
- Theoretical Mathematics