An upgraded Wheels-and-Whirls Theorem for 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:
2012

Citing 12
Cited 0

On inequivalent representations of matroids over finite fields

Journal of Combinatorial Theory Series B
On the structure of 3-connected matroids and graphs

European Journal of Combinatorics
Matroid 4-connectivity: a deletion-contraction theorem

Journal of Combinatorial Theory Series B
A chain theorem for 4-connected matroids

Journal of Combinatorial Theory Series B
The structure of the 3-separations of 3-connected matroids

Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
A Splitter Theorem for Internally 4-Connected Binary Matroids

SIAM Journal on Discrete Mathematics
The structure of 3-connected matroids of path width three

European Journal of Combinatorics
The structure of the 3-separations of 3-connected matroids II

European Journal of Combinatorics
Wild triangles in 3-connected matroids

Journal of Combinatorial Theory Series B
Generating weakly 4-connected matroids

Journal of Combinatorial Theory Series B
A chain theorem for internally 4-connected binary matroids

Journal of Combinatorial Theory Series B
Towards a splitter theorem for internally 4-connected binary matroids

Journal of Combinatorial Theory Series B

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let M be a 3-connected matroid that is not a wheel or a whirl. In this paper, we prove that M has an element e such that M\e or M/e is 3-connected and has no 3-separation that is not equivalent to one induced by M.