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- W3136162914 abstract "A graded ideal I in $$mathbb {K}[x_1,ldots ,x_n]$$ , where $$mathbb {K}$$ is a field, is said to have almost maximal finite index if its minimal free resolution is linear up to the homological degree $$mathrm {pd}(I)-2$$ , while it is not linear at the homological degree $$mathrm {pd}(I)-1$$ , where $$mathrm {pd}(I)$$ denotes the projective dimension of I. In this paper, we classify the graphs whose edge ideals have this property. This in particular shows that for edge ideals the property of having almost maximal finite index does not depend on the characteristic of $$mathbb {K}$$ . We also compute the nonlinear Betti numbers of these ideals. Finally, we show that for the edge ideal I of a graph G with almost maximal finite index, the ideal $$I^s$$ has a linear resolution for $$sge 2$$ if and only if the complementary graph $$bar{G}$$ does not contain induced cycles of length 4." @default.
- W3136162914 created "2021-03-29" @default.
- W3136162914 creator A5064380288 @default.
- W3136162914 date "2021-03-22" @default.
- W3136162914 modified "2023-10-03" @default.
- W3136162914 title "Edge ideals with almost maximal finite index and their powers" @default.
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- W3136162914 doi "https://doi.org/10.1007/s10801-021-01032-y" @default.
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