Every shellable d-dimensional simplicial complex with at most d+3 vertices is extendably shellable, proved through exposed-edge deletions in chordal graphs.
Bj¨orner, The homology and shellability of matroids and geometric lattices , in: N
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Extendable shellability for $d$-dimensional complexes on $d+3$ vertices
Every shellable d-dimensional simplicial complex with at most d+3 vertices is extendably shellable, proved through exposed-edge deletions in chordal graphs.