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

Abstract

We prove that for all $d\ge 1$ 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.

6 pages; V2: corrections and minor revisions, incorporating comments from referees