PARTIAL COLORING, VERTEX DECOMPOSABILITY, AND SEQUENTIALLY COHEN-MACAULAY SIMPLICIAL COMPLEXES
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 Δχ from a coloring χ of...
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| Published in: | Journal of commutative algebra Vol. 7; no. 3; pp. 337 - 352 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Rocky Mountain Mathematics Consortium
01-09-2015
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| Online Access: | Get full text |
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| 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 Δχ from a coloring χ of a subset of the vertices of Δ 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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| ISSN: | 1939-0807 1939-2346 1939-2346 |
| DOI: | 10.1216/JCA-2015-7-3-337 |