Abstract
Given integers r and b with \(1 \le b \le r\), a finite simple connected graph G for which \(\mathrm{reg}(S/I(G)) = r\) and the number of extremal Betti numbers of S / I(G) is equal to b will be constructed.
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Hibi, T., Kimura, K. & Matsuda, K. Extremal Betti numbers of edge ideals. Arch. Math. 113, 149–155 (2019). https://doi.org/10.1007/s00013-019-01322-9
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DOI: https://doi.org/10.1007/s00013-019-01322-9