The regularity \({\text {reg}}R(I(G))\) of the Rees ring R(I(G)) of the edge ideal I(G) of a finite simple graph G is studied. It is shown that, if R(I(G)) is normal, one has \({\text {mat}}(G) \le {\text {reg}}R(I(G)) \le {\text {mat}}(G) + 1\), where \({\text {mat}}(G)\) is the matching number of G. In general, the induced matching number is a lower bound for the regularity, which can be shown by applying the squarefree divisor complex.

中文翻译：

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边理想的里斯代数的匹配数和正则性

研究了有限简单图G的边缘理想I（G）的Rees环R（I（G））的正则性\（{\ text {reg}} R（I（G））\）。结果表明，如果R（I（G（））是正常的，则具有\（{\ text {mat}}（G）\ le {\ text {reg}} R（I（G））\ le {\ text {mat}}（G）+ 1 \），其中\（{\ text {mat}}（G）\）是G的匹配数。通常，诱导匹配数是规则性的下限，可以通过应用平方无因数除数来显示。