@article{c997c29ca79d4f73a7ee9c2ee5b4438b,

title = "The projective dimension of the edge ideal of a very well-covered graph",

abstract = "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.",

author = "Kyouko Kimura and Naoki Terai and Siamak Yassemi",

note = "Funding Information: Kimura was partially supported by JSPS Grant-in-Aid for Young Scientists (B) 24740008/15K17507. Terai was partially supported by JSPS Grant-in-Aid (C) 26400049 and thanks the American Institute of Mathematics for giving the chance to participate in SQuaRE Ordinary powers and symbolic powers. Yassemi was partially supported by a grant from University of Tehran. The authors thank the referee for many comments Publisher Copyright: {\textcopyright} 2017 by The Editorial Board of the Nagoya Mathematical Journal.",

year = "2018",

month = jun,

day = "1",

doi = "10.1017/nmj.2017.7",

language = "English",

volume = "230",

pages = "160--179",

journal = "Nagoya Mathematical Journal",

issn = "0027-7630",

publisher = "Nagoya University",

}