The regular matroids with no 5-wheel minor
For r in \(\{\) 3,4\(\}\), the class of binary matroids with no minor isomorphic to M(\({\mathcal W}_ r)\), the rank-r wheel, has an easily- described structure. This paper determines all graphs with no \({\mathcal W}_ 5\)-minor and uses this to show that the class of regular matroids with no M(\({\mathcal W}_ 5)\)-minor also has a relatively simple structure. It is deduced from the graph result that a simple n-vertex graph having no \({\mathcal W}_ 5\)-minor has chromatic number at most 5. Moreover, such a graph has at most 3n-5 edges if \(n\equiv 2\) (mod 3) and has at most 3n-6 edges otherwise.
scientific article; zbMATH DE number 4016914
scientific article