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math.CO2025
A High-Dimensional Extension of Wagner's Theorem and the Geometrization of Hypergraphs
Qiming Fang, Sihong Shao
This paper introduces a geometric representation of hypergraphs by representing hyperedges as simplices. Building on this framework, we employ homotopy groups to analyze the topolo…
math.CO2024
Geometrization of Graphs: Towards Bounding the Chromatic Number via High-Dimensional Embedding
Qiming Fang, Sihong Shao
We establish a geometric framework by transforming a graph into a -dimensional CW complex . This construction is achieved by systematically attaching -sph…