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Independence Complexes of Kneser Graphs

Ziqin Feng ⟨zzf0006@auburn.edu⟩

Abstract:

We will discuss the topological properties of the independence complex of Kneser graphs, Ind(KG(n,k)), with n3 and k1. By identifying one kind of maximal simplices through projective planes, we obtain homology generators for the 6-dimensional homology of the complex Ind(KG(3,k)). Using cross-polytopal generators, we provide lower bounds for the rank of p-dimensional homology of the complex Ind(KG(n,k)) where p=1/2(2n+k2n).

Scheduled for: 2025-03-08 03:35 PM: Ziqin Feng (virtual) in Forbes 1022

Status: Accepted

Collection: Applied Topology

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