Open Access
FALL 2015 Partial coloring, vertex decomposability and sequentially Cohen-Macaulay simplicial complexes
Jennifer Biermann, Christopher A. Francisco, Huy Tài Hà, Adam Van Tuyl
J. Commut. Algebra 7(3): 337-352 (FALL 2015). DOI: 10.1216/JCA-2015-7-3-337


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.


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Jennifer Biermann. Christopher A. Francisco. Huy Tài Hà. Adam Van Tuyl. "Partial coloring, vertex decomposability and sequentially Cohen-Macaulay simplicial complexes." J. Commut. Algebra 7 (3) 337 - 352, FALL 2015.


Published: FALL 2015
First available in Project Euclid: 14 December 2015

zbMATH: 1328.05207
MathSciNet: MR3433985
Digital Object Identifier: 10.1216/JCA-2015-7-3-337

Primary: 05A15 , 05E45 , 13F55

Keywords: sequentially Cohen-Macaulay , simplicial complex , vertex decomposable , whiskers

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.7 • No. 3 • FALL 2015
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