Proof of two Maurer's conjectures on basis graphs of matroids

@article{Chalopin2012ProofOT,
  title={Proof of two Maurer's conjectures on basis graphs of matroids},
  author={J{\'e}r{\'e}mie Chalopin and Victor Chepoi and Damian Osajda},
  journal={CoRR},
  year={2012},
  volume={abs/1212.6879}
}
We characterize 2–dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of a (disproved) conjecture by Stephen Maurer (Conjecture 3 of S. Maurer, Matroid basis graphs I, JCTB 14 (1973), 216–240). We also establish Conjecture 1 from the same paper about the redundancy of the conditions in the characterization of basis graphs. We indicate positive-curvature-like aspects of… CONTINUE READING