We study the connections between the notions of combinatorial discrepancy and graph degeneracy. In particular, we prove that the maximum discrepancy over all subgraphs of a graph of the neighborhood set system of is sandwiched between and , where denotes the degeneracy of . We extend this result to inequalities relating weak coloring numbers and discrepancy of graph powers and deduce a new characterization of bounded expansion classes.

中文翻译：

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 差异和稀疏性


我们研究组合差异和图简并性概念之间的联系。特别是，我们证明 的邻域集系统图的所有子图的最大差异夹在 和 之间，其中表示 的简并性。我们将此结果扩展到与弱着色数和图幂差异相关的不等式，并推导出有界扩展类的新特征。