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Edgewise strongly shellable clutters. (English) Zbl 1377.05201

Summary: When \(\mathcal{C}\) is a chordal clutter in the sense of R. Woodroofe [Electron. J. Comb. 18, No. 1, Research Paper P208, 20 p. (2011; Zbl 1236.05213)] or E. Emtander [Math. Scand. 106, No. 1, 50–66 (2010; Zbl 1183.05053)], we show that the complement clutter is edgewise strongly shellable. When \(\mathcal{C}\) is indeed a finite simple graph, we provide additional characterization of chordal graphs from the point of view of strong shellability. In particular, the generic graph \(G_T\) of a tree is shown to be bi-strongly shellable.

MSC:

05E40 Combinatorial aspects of commutative algebra
05E45 Combinatorial aspects of simplicial complexes
13C14 Cohen-Macaulay modules
05C65 Hypergraphs
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