We give two graph theoretical characterizations of tope graphs of (complexes of) oriented matroids. The first is in terms of excluded partial cube minors, the second is that all antipodal subgraphs are gated. Corollaries include a characterization of topes of oriented matroids due to da Silva, another one of Handa, a characterization of lopsided systems due
to Lawrence, and an intrinsic characterization of tope graphs of affine oriented matroids. Moreover, we obtain purely graph theoretic polynomial time recognition algorithms for tope graphs.
I will try to furthermore give some perspectives on classical problems as Las Vergnas simplex conjecture in terms of Metric Graph Theory.
Based on joint work with H.-J; Bandelt, V. Chepoi, and T. Marc.
Apr 29, 2019 | 02:15 PM
Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
Room MA 041 (Ground Floor)