On independence complexes of graph products

2025/05/09 by Bravo, Andrés Carnero · 1 citation
#05C76 #05E45 #55P15 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.06457

Abstract

We study the independence complexes of graph products where at least one factor is a path. We also analyze the complexes of their induced subgraphs. We determine the homotopy type of the independence complex of the graphs P_n× P_m, P_n\boxtimes P₂, P_n\boxtimes P₃ and P_n\boxtimes P₄. We also focus in the independence complexes of the induced subgraphs of P_n× P₃, P_n\boxtimes P₂, P_n\boxtimes P₃, P_n\boxtimes P₄ and some lexicographic products G∘ H.

Citations

• On the Connectivity of the Vietoris-Rips Complex of a Hypercube Graph
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Cited by

• Closed neighborhood complexes of graphs

Related

• Independence Complex of the Lexicographic Product of a Forest
• Homotopy type of the independence complex of some categorical products of graphs
• Independence complexes of wedge of graphs
• On the homology of independence complexes
• Splittings of independence complexes and the powers of cycles