Work

Embracing exchange sequences and oriented matroid polyhedron diameter

Year: 2026

Type: preprint

Abstract: We reduce the embracing exchange distance of bases of oriented matroids to the metric of oriented matroid polyhedra. This allows us to disprove recent conjectures of Caoduro, Khodamoradi, Paat, and Shepherd and of Bérczi and Nádor. On the other hand, we show that any two embracing bases of an oriented matroid of rank $r$ can be transformed into each other in at most $2r^{\log_2(r)+3}$ steps and in at most $r$ steps in a graphic oriented matroid or a Lawrence oriented matroid, thus confirming the conjecture in these cases.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2606.19573

Authors: Bérczi, Kristóf, Knauer, Kolja, Montejano, Luis Pedro, Nádor, Benedek

Institutions: Centre de Recerca Matemàtica, Universitat de Barcelona, Universitat Rovira i Virgili

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Ministerio de Ciencia e Innovación, European Regional Development Fund, Agencia Estatal de Investigación

Awards: G1186134865, G1401168639, G14461421, G2660406951, G3480869486, G3518538256, G4274939422, G464105488, G5292200796, G6033112984, G6307970414, G7084143925, G7249198066, Metric minors in graphs, G7926210262, G84477964, G8920660035

OpenAlex ID: W7165393565

Cites:

Cited by: 1

Related to: 10