Graph representations of a bicircular matroid
The bicircular matroid \(B(G)\) of a graph \(G\) is known as a transversal matroid. The author discusses the graphs which represent the same bicircular matroid. The main results are: 1. The natural presentation of the bicircular matroid of a graph \(G\) determines \(G\) up to an isomorphism. 2. If \(G\) is a graph with no parallel edges and minimum degree at least three and \(G'\) is another graph such that \(B(G)= B(G')\), then \(G\) and \(G'\) are isomorphic. 3. Given any presentation for a bicircular matroid \(M\), then, up to isomorphism, the author describes an algorithm determining all the graphs \(G\) representing \(M\) such that \(B(G)=M\). 4. The description of the graphs arising from the minimal presentations of a bicircular matroid.
scientific article; zbMATH DE number 1758380