44 citations · 77 across the 17 of their papers we have counts for
29 papers
Skeleton Chordalities
Bruno Benedetti, Marta Pavelka
We study new higher-dimensional analogs of graph chordality and review the existing ones. Our main results for simplicial complexes are: (1) skeleton-E-chordal $Δ…
Higher-dimensional counterexamples to Hamiltonicity
Bruno Benedetti, Marta Pavelka
For , we show that all graphs of -polytopes have a Hamiltonian line graph if and only if : We exhibit a graph of a -polytope on vertices whose line gr…
Random Simple-Homotopy Theory
Bruno Benedetti, Crystal Lai, Davide Lofano +1
We implement an algorithm RSHT (Random Simple-Homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding su…
2-LC triangulated manifolds are exponentially many
Bruno Benedetti, Marta Pavelka
We introduce "-LC triangulated manifolds" as those triangulations obtainable from a tree of -simplices by recursively identifying two boundary -faces whose intersectio…
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…
Sparse handlebody decompositions and non-finiteness of
Karim Adiprasito, Bruno Benedetti
We prove that a PL manifold admits a handle decomposition into handles of index if and only if is -stacked, i.e., it admits a PL triangulation in which all …
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…
A Cheeger-type exponential bound for the number of triangulated manifolds
Karim Adiprasito, Bruno Benedetti
In terms of the number of triangles, it is known that there are more than exponentially many triangulations of surfaces, but only exponentially many triangulations of surfaces with…
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…
Mogami manifolds, nuclei, and 3D simplicial gravity
Bruno Benedetti
Mogami introduced in 1995 a large class of triangulated 3-dimensional pseudomanifolds, henceforth called "Mogami pseudomanifolds". He proved an exponential bound for the size of th…
Regularity of Line Configurations
Bruno Benedetti, Michela Di Marca, Matteo Varbaro
We show that in arithmetically-Gorenstein line arrangements with only planar singularities, each line intersects the same number of other lines. This number has an algebraic interp…
Regulating Hartshorne's connectedness theorem
Bruno Benedetti, Barbara Bolognese, Matteo Varbaro
A classical theorem by Hartshorne states that the dual graph of any arithmetically Cohen--Macaulay projective scheme is connected. We give a quantitative version of Hartshorne's re…
Extremal examples of collapsible complexes and random discrete Morse theory
Karim A. Adiprasito, Bruno Benedetti, Frank H. Lutz
We present extremal constructions connected with the property of simplicial collapsibility. (1) For each , there are collapsible (and shellable) simplicial -complexes w…
Linear embeddings of contractible and collapsible complexes
Karim A. Adiprasito, Bruno Benedetti
(1) We show that if a presentation of the trivial group is "hard to trivialize", in the sense that lots of Tietze moves are necessary to transform it into the trivial presentation,…
On the dual graph of Cohen-Macaulay algebras
Bruno Benedetti, Matteo Varbaro
Given a projective algebraic set X, its dual graph G(X) is the graph whose vertices are the irreducible components of X and whose edges connect components that intersect in codimen…
Knots in collapsible and non-collapsible balls
Bruno Benedetti, Frank H. Lutz
We construct the first explicit example of a simplicial 3-ball B_{15,66} that is not collapsible. It has only 15 vertices. We exhibit a second 3-ball B_{12,38} with 12 vertices tha…
Random Discrete Morse Theory and a New Library of Triangulations
Bruno Benedetti, Frank H. Lutz
1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete M…
The Hirsch conjecture holds for normal flag complexes
Karim Alexander Adiprasito, Bruno Benedetti
Using an intuition from metric geometry, we prove that any flag and normal simplicial complex satisfies the non-revisiting path conjecture. As a consequence, the diameter of its fa…
Smoothing discrete Morse theory
Bruno Benedetti
After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and…
Subdivisions, shellability, and collapsibility of products
Karim Alexander Adiprasito, Bruno Benedetti
We prove that the second derived subdivision of any rectilinear triangulation of any convex polytope is shellable. Also, we prove that the first derived subdivision of every rectil…
Tight complexes in 3-space admit perfect discrete Morse functions
Karim Adiprasito, Bruno Benedetti
In 1967, Chillingworth proved that all convex simplicial 3-balls are collapsible. Using the classical notion of tightness, we generalize this to arbitrary manifolds: We show that a…
Collapsibility of CAT(0) spaces
Karim Adiprasito, Bruno Benedetti
Collapsibility is a combinatorial strengthening of contractibility. We relate this property to metric geometry by proving the collapsibility of any complex that is CAT(0) with a me…
Discrete Morse Theory Is At Least As Perfect As Morse Theory
Bruno Benedetti
In bounding the homology of a manifold, Forman's Discrete Morse theory recovers the full precision of classical Morse theory: Given a PL triangulation of a manifold that admits a M…
Discrete Morse Theory for Manifolds with Boundary
Bruno Benedetti
We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain "…