Bruno Benedetti

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20242026

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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) $I^$ skeleton-E-chordal $\Rightarrow$ $…

math.CO2025

Higher-dimensional counterexamples to Hamiltonicity

Bruno Benedetti, Marta Pavelka

For $d \geq 2$ , we show that all graphs of $d$ -polytopes have a Hamiltonian line graph if and only if $d \neq = 3$ : We exhibit a graph of a $3$ -polytope on $252$ vertices whose line gr…