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On independence complexes of graph products (2505.06457v1)
Published 9 May 2025 in math.CO and math.AT
Abstract: We study the independence complex for graph products where at least one of the factors is a path as well as the complexes for their induced subgraphs. We calculate the homotopy type of the independence complex of the graphs $P_n\times P_m$, $P_n\boxtimes P_2$, $P_n\boxtimes P_3$ and $P_n\boxtimes P_4$. We also focus in the independence complexes of the induced subgraphs of $P_n\times P_3$, $P_n\boxtimes P_2$, $P_n\boxtimes P_3$, $P_n\boxtimes P_4$ and some lexicographic products.
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