Triples in Matroid Circuits

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Abstract

Watkins and Mesner characterized edge-triples of a graph which are not in any circuit, and Chakravarti and Robertson solved the dual problem of edge-triples not in a bond. Here we give a common generalization, solving the problem for all binary matroids. Our main result is that if e, f, g are elements of a 3-connected, internally 4-connected binary matroid, then there is a circuit containing e, f, g, unless either {e, f, g} is a cocircuit, or the matroid is graphic and e, f, g are edges of the graph with a common vertex. The more general non-binary problem is still open.

Original languageEnglish (US)
Pages (from-to)177-185
Number of pages9
JournalEuropean Journal of Combinatorics
Volume7
Issue number2
DOIs
StatePublished - Jan 1 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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