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math.CO2021
Hamiltonian paths, unit-interval complexes, and determinantal facet ideals
Bruno Benedetti, Lisa Seccia, Matteo Varbaro
We study d-dimensional generalizations of three mutually related topics in graph theory: Hamiltonian paths, (unit) interval graphs, and binomial edge ideals. We provide partial hig…
math.CO2019
Non-ridge-chordal complexes whose clique complex has shellable Alexander dual
Bruno Benedetti, Davide Bolognini
A recent conjecture that appeared in three papers by Bigdeli--Faridi, Dochtermann, and Nikseresht, is that every simplicial complex whose clique complex has shellable Alexander dua…
math.CO2017
Barycentric subdivisions of convex complexes are collapsible
Karim Adiprasito, Bruno Benedetti
A classical question in PL topology, asked among others by Hudson, Lickorish, and Kirby, is whether every linear subdivision of the d-simplex is simplicially collapsible. The answe…