We say that two elements e, f of a binary matroid M are ‘adjacent’ if there is no minor of M isomorphic to ℳ(K4) which uses both e and f and in which they correspond to opposite edges. We give a good characterization of when two elements are adjacent. In particular, we show that if M is 4-connected, elements e, f are adjacent if and only if M is either graphic or cographic and the elements correspond to adjacent edges of the graph. We deduce a theorem about disjoint paths in graphs.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics