The projective dimension of the edge ideal of a very well-covered graph
The projective dimension of the edge ideal of a very well-covered graph
复制标题
覆盖良好的图的理想边的投影维数
DOI：
10.1017/nmj.2017.7
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发表时间：
2017
影响因子：
0.8
通讯作者：
Siamak Yassemi
中科院分区：
文献类型：
--
作者：
Kyouko Kimura;Naoki Terai;Siamak Yassemi
非常好覆盖图是覆盖数为顶点数一半的未混合图。我们构造了Cohen-Macaulay非常好覆盖图的覆盖理想的一个显式极小自由分解。利用这一解决方案，我们刻画了一个非常好的覆盖图的边缘理想的投影维数的一个成对不相交的完全二部子图的图。我们还证明了一个非常好的覆盖图的边理想的符号幂的投影维数关于指数的非减性质。
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 -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.