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

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