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arxiv: 2505.23293 · v3 · pith:R67QLGV4new · submitted 2025-05-29 · 🧮 math.CO · math.GR· math.MG

Cell structure of mediangle graphs

Victor Chepoi , Anthony Genevois , Kolja Knauer This is my paper
classification 🧮 math.CO math.GRmath.MG
keywords graphsmedianglecellcomplexcomplexescoxetermatroidsoriented
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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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