Partial coloring, vertex decomposability, and sequentially Cohen-Macaulay simplicial complexes Academic Article uri icon

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abstract

  • 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 to build 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.

authors

  • Van Tuyl, Adam
  • Biermann, Jennifer
  • Francisco, Christopher A
  • Hà, Huy Tài
  • Tuyl, Adam Van

publication date

  • September 1, 2015