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Regular partitions of gentle graphs
arXiv - CS - Discrete Mathematics Pub Date : 2020-03-26 , DOI: arxiv-2003.11692
Yiting Jiang; Jaroslav Nesetril; Patrice Ossona de Mendez; Sebastian Siebertz

Szemeredi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the theory of (structural) sparsity, which leads to alternative proofs, refinements and solutions of open problems. It is interesting to note that many of these classes present challenging problems. Nevertheless, from the point of view of regularity lemma type statements, they appear as "gentle" classes.
更新日期:2020-03-27

 

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