Application of hypergraph Hoffman's bound to intersecting families
Norihide Tokushige

TL;DR
This paper applies hypergraph Hoffman's bound via the Filmus-Golubev-Lifshitz method to analyze intersecting families, providing new bounds and stability results for measure versions of classical combinatorial theorems.
Contribution
It introduces a novel application of Hoffman's bound to hypergraphs for intersecting families, extending stability results in measure versions of Erdős-Ko-Rado.
Findings
Bound the independence number of hypergraphs using the method.
Prove a stability result for measure versions of Erdős-Ko-Rado.
Address problems on multiply intersecting families with biased measure.
Abstract
Using the Filmus-Golubev-Lifshitz method to bound the independence number of a hypergraph, we solve some problems concerning multiply intersecting families with biased measure. Among other results we obtain a stability result of a measure version of the Erdos-Ko-Rado theorem for multiply intersecting families.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Advanced Topology and Set Theory
