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arXiv · 0904.4927

A simple regularization of graphs

Yoshiyasu Ishigami
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Abstract

The well-known regularity lemma of E. Szemerédi for graphs (i.e. 2-uniform hypergraphs) claims that for any graph there exists a vertex partition with the property of quasi-randomness. We give a simple construction of such a partition. It is done just by taking a constant-bounded number of random vertex samplings only one time (thus, iteration-free). Since it is independent from the definition of quasi-randomness, it can be generalized very naturally to hypergraph regularization. In this expository note, we show only a graph case of the paper [I] on hypergraphs, but may help the reader to access [I].

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Yoshiyasu Ishigami. 2009-04-30. A simple regularization of graphs. https://arxiv.org/abs/0904.4927

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