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arXiv · 1209.3008

Partial coloring, vertex decomposability, and sequentially Cohen-Macaulay simplicial complexes

Jennifer Biermann·Christopher A. Francisco·Huy Tài Hà·Adam Van Tuyl
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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.

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Jennifer Biermann, Christopher A. Francisco, Huy Tài Hà, Adam Van Tuyl. 2012-09-13. Partial coloring, vertex decomposability, and sequentially Cohen-Macaulay simplicial complexes. https://arxiv.org/abs/1209.3008

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