In attempting to understand how combinatorial modifications alter algebraic properties of monomial ideals, several authors have investigated the process of adding ``whiskers'' to graphs. In this paper, we study a similar construction for building a simplicial complex $\Delta_\chi$ from a coloring $\chi$ of a subset of the vertices of $\Delta$ and give necessary and sufficient conditions for this construction to produce vertex decomposable simplicial complexes. We apply this work to strengthen and give new proofs about sequentially Cohen-Macaulay edge ideals of graphs.
"Partial coloring, vertex decomposability and sequentially Cohen-Macaulay simplicial complexes." J. Commut. Algebra 7 (3) 337 - 352, FALL 2015. https://doi.org/10.1216/JCA-2015-7-3-337