THE PROJECTIVE DIMENSION OF THE EDGE IDEAL OF A VERY WELL-COVERED GRAPH
| Autor: | Naoki Terai, Kyouko Kimura, Siamak Yassemi |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Well-covered graph
General Mathematics Wagner graph 010102 general mathematics Voltage graph 0102 computer and information sciences 01 natural sciences Gray graph Simplex graph Geometric graph theory law.invention Combinatorics 010201 computation theory & mathematics law Petersen graph Line graph 0101 mathematics Mathematics |
| Zdroj: | Nagoya Mathematical Journal. 230:160-179 |
| ISSN: | 2152-6842 0027-7630 |
| Popis: | A very well-covered graph is an unmixed graph whose covering number is half of the number of vertices. We construct an explicit minimal free resolution of the cover ideal of a Cohen–Macaulay very well-covered graph. Using this resolution, we characterize the projective dimension of the edge ideal of a very well-covered graph in terms of a pairwise$3$-disjoint set of complete bipartite subgraphs of the graph. We also show nondecreasing property of the projective dimension of symbolic powers of the edge ideal of a very well-covered graph with respect to the exponents. |
| Databáze: | OpenAIRE |
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