3 citations · 5 across the 7 of their papers we have counts for
7 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…
Chordality, syzygies, and shellability for hypergraphic analogues of interval graphs
Anton Dochtermann, Bennet Goeckner, Marta Pavelka
Interval graphs are a special class of chordal graphs, and hence have connections to commutative algebra via Fröberg's theorem that characterizes linear resolutions of squarefree q…
Vertex orders in higher dimensions
Bennet Goeckner, Marta Pavelka
Unit interval and interval complexes are higher-dimensional generalizations of unit interval and interval graphs, respectively. We show that strongly connected unit interval comple…
A conditional lower bound for the Turán number of spheres
Andrew Newman, Marta Pavelka
We consider the hypergraph Turán problem of determining , the maximum number of facets in a -dimensional simplicial complex on vertices that does not co…
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…
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…
On-line algorithms for multiplication and division in real and complex numeration systems
Christiane Frougny, Marta Pavelka, Edita Pelantova +1
A positional numeration system is given by a base and by a set of digits. The base is a real or complex number such that , and the digit set is a finite set of digit…