Homotopy types of Vietoris-Rips complexes of Hypercube Graphs

2023/05/11 by Ziqin Feng, Feng, Ziqin · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2305.07084

Abstract

We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs at scale 3. We represent the vertices in the hypercube graph Q_m as the collection of all subsets of [m]=\1, 2, …, m\ and equip Q_m with the metric using symmetric difference distance. It is proved in \citeAA22 that the Vietoris-Rips complexes of hypercube graphs Q_m at scale 2, VR(Q_m; 2), is homotopy equivalent to c_m-many spheres with dimension 3 where c_m=∑_0≤ j< i

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