@article {IOPORT.04016914, author = {Oxley, James G.}, title = {The regular matroids with no 5-wheel minor.}, year = {1989}, journal = {Journal of Combinatorial Theory. Series B}, volume = {46}, number = {3}, issn = {0095-8956}, pages = {292-305}, publisher = {Elsevier Science (Academic Press), San Diego, CA}, doi = {10.1016/0095-8956(89)90051-8}, abstract = {For r in $\{$ 3,4$\}$, the class of binary matroids with no minor isomorphic to M(${\cal W}\sb r)$, the rank-r wheel, has an easily- described structure. This paper determines all graphs with no ${\cal W}\sb 5$-minor and uses this to show that the class of regular matroids with no M(${\cal W}\sb 5)$-minor also has a relatively simple structure. It is deduced from the graph result that a simple n-vertex graph having no ${\cal W}\sb 5$-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.}, identifier = {04016914}, }