Abstract
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.
Original language | English (US) |
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Pages (from-to) | 171-176 |
Number of pages | 6 |
Journal | European Journal of Combinatorics |
Volume | 7 |
Issue number | 2 |
DOIs | |
State | Published - 1986 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics