Extendable Shellability for $d$-Dimensional Complexes on $d+3$ Vertices

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

Abstract: We prove that for all $d \geq 1$, a shellable $d$-dimensional 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.