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Edge ideals of gapfree graphs with matching number
Nursel Erey, Tài Huy Hà, Takayuki Hibi +2
We prove that if is a gapfree graph with matching number , then every power , , of its edge ideal has linear quotients, and hence a linear resolution. Our ap…
Depth of edge ideals and vertex connectivity of finite graphs
Takayuki Hibi, Seyed Amin Seyed Fakhari
Let be a finite graph on and its vertex connectivity. Let denote the polynomial ring in variables over a field an…
Pseudo-Gorenstein Graphs
Takayuki Hibi, Selvi Kara, Dalena Vien
Motivated by pseudo-Gorenstein rings in commutative algebra, introduced by Herzog et al., we define pseudo-Gorenstein graphs and classify them in several natural graph famili…
Binomial edge ideals of Cameron-Walker graphs
Takayuki Hibi, Sara Saeedi Madani
Let be a Cameron--Walker graph on vertices and the binomial edge ideal of . Let denote the polynomial ring in variables over a field. It is shown that the…
Cohen-Macaulay squares of edge ideals
Sara Faridi, Takayuki Hibi
Let be a finite graph and its edge ideal. We give a full description of the Stanley--Reisner complex of the polarization of , naturally introducing the tools of…
Gapfree graphs and powers of edge ideals with linear quotients
Nursel Erey, Sara Faridi, Tài Huy Hà +3
Let be the edge ideal of a gapfree graph . An open conjecture of Nevo and Peeva states that has linear resolution for . We present a promising approach t…
Resolution and Betti numbers of Vertex cover ideals
Tài Huy Hà, Takayuki Hibi
The vertex cover ideal of a finite graph is studied. We characterize when a Cohen--Macaulay vertex cover ideal has a Scarf minimal free resolution. Furthermore, b…
Scarf complexes of graphs and their powers
Sara Faridi, Tài Huy Hà, Takayuki Hibi +1
Every multigraded free resolution of a monomial ideal I contains the Scarf multidegrees of I. We say I has a Scarf resolution if the Scarf multidegrees are sufficient to describe a…