LC reductions yield isomorphic simplicial complexes
Jiřı́ Matoušek · Libraries and Cultural Resources (University of Calgary) · 2007
We say that a vertex $v$ of a finite simplicial complex $K4 is LC-removable if the link of $v$ is a cone, and that $K$ is LC-irreducible if it has no LC-removable vertices. Answering a question of Civan and Yal\,cın [J. Comb. Theory Ser. A(2007), doi:10.1016/j.jcta.2007.02.001], we prove that all LC-irreducible simplicial complexes that can be obtained from a given $K$ by repeatedly deleting LC-removable vertices (plus all simplices containing them) are isomorphic.