Adjacency in Binary Matroids

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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 languageEnglish (US)
Pages (from-to)171-176
Number of pages6
JournalEuropean Journal of Combinatorics
Issue number2
StatePublished - 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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