Colorings of simplicial complexes and vertex decomposability 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. The first and the fourth authors developed a similar construction to build a vertex decomposable simplicial complex $\Delta_\chi$ from a coloring $\chi$ of the vertices of a simplicial complex $\Delta$. In this paper, we study this construction for colorings of subsets of the vertices, and give necessary and sufficient conditions for this construction to produce vertex decomposable simplicial complexes. Using combinatorial topology, we strengthen and give new proofs for results of the second and third authors about sequentially Cohen-Macaulay edge ideals that were originally proved using algebraic techniques.

authors

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