3 papers
math.CO2026
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…
math.CO2026
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…
math.CO2024
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…