Extendable shellability for $d$-dimensional complexes on $d+3$ vertices

Jared Culbertson, Anton Dochtermann, Dan P. Guralnik, Peter F. Stiller

Published 2019-08-20Version 1

We prove that for all $d \geq 1$ a shellable $d$-dimensional simplicial complex with at most $d+3$ vertices is extendably shellable. The proof involves considering the structure of `exposed' edges in chordal graphs as well as a connection to linear quotients of quadratic monomial ideals.