Weighted digraphs and tropical cones

Michael Joswig*, Georg Loho

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)
3 Downloads (Pure)


This paper is about the combinatorics of finite point con-figurations in the tropical projective space or, dually, of ar-rangements of finitely many tropical hyperplanes. Moreover, arrangements of finitely many tropical halfspaces can be con-sidered via coarsenings of the resulting polyhedral decompo-sitions of ℝd. This leads to natural cell decompositions of the tropical projective space TPd-1min. Our method is to employ a known class of ordinary convex polyhedra naturally associated with weighted digraphs. This way we can relate to and use re-sults from combinatorics and optimization. One outcome is the solution of a conjecture of Develin and Yu (2007).

Original languageEnglish
Pages (from-to)304-343
Number of pages40
JournalLinear algebra and its applications
Publication statusPublished - 15 Jul 2016
Externally publishedYes


  • Braid cones
  • Directed graphs
  • Order polytopes
  • Regular subdivisions
  • Tropical convexity


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