Partial coloring, vertex decomposability and sequentially Cohen-Macaulay simplicial complexes.(English)Zbl 1328.05207

Summary: 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.

MSC:

 05E45 Combinatorial aspects of simplicial complexes 05A15 Exact enumeration problems, generating functions 13C14 Cohen-Macaulay modules 13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
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References:

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