Internally 4-Connected Binary Matroids with Every Element in Three Triangles

Abstract

Let M be an internally 4-connected binary matroid with every element in exactly three triangles. Then M has at least four elements e such that si(M/e) is internally 4-connected. This technical result is a crucial ingredient in Abdi and Guenin’s theorem determining the minimally non-ideal binary clutters that have a triangle.

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Acknowledgements

The authors thank the referees for numerous suggestions that both corrected errors and improved the exposition.

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Correspondence to Carolyn Chun or James Oxley.

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Chun, C., Oxley, J. Internally 4-Connected Binary Matroids with Every Element in Three Triangles. Combinatorica 39, 825–845 (2019). https://doi.org/10.1007/s00493-019-3720-1

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Mathematics Subject Classification (2010)

  • 05B35
  • 52B40