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arXiv · 2505.23293

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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Victor Chepoi, Anthony Genevois, Kolja Knauer. 2026-05-30. Cell structure of mediangle graphs. https://arxiv.org/abs/2505.23293

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