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Tight Hamilton cycles with high discrepancy

组织者

本杰明·苏达科夫

演讲者

Stefan Glock

时间

2024年05月07日 17:05 至 18:15

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

In discrepancy theory, the basic question is whether a structure can be partitioned in a balanced way, or if there is always some “discrepancy” no matter how the partition is made. In the context of graph theory, a well-studied question is whether for a given host graph, any 2-colouring of its edges must contain a specified subgraph "with high discrepancy", meaning that within this subgraph one of the colour classes is significantly larger than the other. We initiate the study of such questions for hypergraphs. Our main result is a discrepancy version of the celebrated theorem of R\"odl, Ruci\'nski and Szemer\'edi on tight Hamilton cycles in Dirac hypergraphs. Joint work with Lior Gishboliner and Amedeo Sgueglia.