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Skeleton Chordalities
We study new higher-dimensional analogs of graph chordality and review the existing ones. Our main results for simplicial complexes are: (1) $Δ$ skeleton-E-chordal $\Rightarrow$ $Δ^\vee$ vertex-decomposable $\Rightarrow$ $Δ$ skeleton-clique-chordal. Moreover, for subflag complexes, $Δ$ skeleton-E-
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