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math.CO2026
Total cut complexes and their duals
Andrés Carnero Bravo
We study the total -cut complexes and their Alexander duals. We give some results about the connectivity in general and in terms of the grith of the graph. For , the hom…
math.CO2026
Independence complexes of generalized Mycielskian graphs
Andrés Carnero Bravo
We show that the homotopy type of the independence complex of the generalized Mycielskian of a graph is determined by the homotopy type of the independence complex of and t…
math.CO2025
On independence complexes of graph products
Andrés Carnero Bravo
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…