On theories of Whitney and Tutte (Q1070237)

By making extensive use of connectivity properties of graphs the author gives new proofs of the following classical results: (1) For nonseparable graphs G, G' the cycle matroids M(G) and M(G') are isomorphic iff G and G' are 2-isomorphic (Whitney); (2) A binary matroid M is graphic iff none of \(F_ 7\), \(F_ 7^*\), \(M^*(K_ 5)\) and \(M^*(K_{3,3})\) is a minor of M (Tutte). The proofs are simpler and shorter and such lend themselves for use in introductory courses on this subject.