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PreprintCC BY-NC-ND 4.0HAL

Cell structure of mediangle graphs

  • Victor Chepoi
  • Anthony Genevois
  • Kolja Knauer
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Abstract

Mediangle graphs are a common generalization of median graphs (1-sekeleta of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter systems). Answering a question motivated from geometric group theory, we show that these graphs can be endowed with the structure of a contractible cell complex. We further show that the cells of this complex are products of simplices and simplicial oriented matroids. A crucial part of the proof identifies bipartite mediangle graphs as tope graphs of finitary Complexes of Oriented Matroids.

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Cite

BibTeXRIS
BibTeX
@misc{chepoi2026cell,
  title = {{Cell structure of mediangle graphs}},
  author = {Victor Chepoi and Anthony Genevois and Kolja Knauer},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  eprint = {2505.23293},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05768723v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Cell structure of mediangle graphs
AU  - Victor Chepoi
AU  - Anthony Genevois
AU  - Kolja Knauer
PY  - 2026
DA  - 2026/09/29
PB  - HAL
UR  - https://hal.science/hal-05768723v1
AB  - Mediangle graphs are a common generalization of median graphs (1-sekeleta of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter systems). Answering a question motivated from geometric group theory, we show that these graphs can be endowed with the structure of a contractible cell complex. We further show that the cells of this complex are products of simplices and simplicial oriented matroids. A crucial part of the proof identifies bipartite mediangle graphs as tope graphs of finitary Complexes of Oriented Matroids.
ER  -