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Obstructions to Shellability

Michelle L. Wachs
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Abstract

We consider a simplicial complex generaliztion of a result of Billera and Meyers that every nonshellable poset contains the smallest nonshellable poset as an induced subposet. We prove that every nonshellable $2$-dimensional simplicial complex contains a nonshellable induced subcomplex with less than $8$ vertices. We also establish CL-shellability of interval orders and as a consequence obtain a formula for the Betti numbers of any interval order.

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Michelle L. Wachs. 1997-07-07. Obstructions to Shellability. https://arxiv.org/abs/math/9707216

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