Abstract.
We consider a simplicial complex generalization of a result of Billera and Myers that every nonshellable poset contains the smallest nonshellable poset as an induced subposet. We prove that every nonshellable two-dimensional simplicial complex contains a nonshellable induced subcomplex with less than eight 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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Received August 7, 1997, and in revised form September 9, 1998.
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Wachs, M. Obstructions to Shellability . Discrete Comput Geom 22, 95–103 (1999). https://doi.org/10.1007/PL00009450
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DOI: https://doi.org/10.1007/PL00009450