Castelnuovo-Mumford regularity is a measure of algebraic complexity of an ideal. Regularity of monomial ideals can be investigated combinatorially. We use a simple graph decomposition and results from structural graph theory to prove, improve and generalize many of the known bounds on regularity of quadratic square-free monomial ideals.

中文翻译：

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二次多项式理想的正则性界

Castelnuovo-Mumford正则性是对理想代数复杂性的度量。单项理想的规律性可以组合研究。我们使用简单的图分解和结构图理论的结果来证明，改进和推广许多关于平方无平方单项理想的正则性的已知界限。