4 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 $…
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…
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…
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…