Wild triangles in 3-connected matroids

Authors:
James Oxley;Charles Semple;Geoff Whittle
Affiliations:
Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA;Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand;School of Mathematical and Computing Sciences, Victoria University, Wellington, New Zealand
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

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Abstract

Let {a,b,c} be a triangle in a 3-connected matroid M. In this paper, we describe the structure of M relative to {a,b,c} when, for all t in {a,b,c}, either M\t is not 3-connected, or M\t has a 3-separation that is not equivalent to one induced by M.