Hypergraph Independent Sets

Author:

CUTLER JONATHAN,RADCLIFFE A. J.

Abstract

The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. There are a variety of types of independent sets in hypergraphs depending on the number of vertices from an independent set allowed in an edge. We say that a subset of vertices isj-independentif its intersection with any edge has size strictly less thanj. The Kruskal–Katona theorem implies that in anr-uniform hypergraph with a fixed size and order, the hypergraph with the mostr-independent sets is the lexicographic hypergraph. In this paper, we use a hypergraph regularity lemma, along with a technique developed by Loh, Pikhurko and Sudakov, to give an asymptotically best possible upper bound on the number ofj-independent sets in anr-uniform hypergraph.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

Cited by 9 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Zeon and Idem-Clifford Formulations of Hypergraph Problems;Advances in Applied Clifford Algebras;2022-10-07

2. Maximizing $2$-Independents Sets in $3$-Uniform Hypergraphs;The Electronic Journal of Combinatorics;2022-07-15

3. Bounds on Threshold Probabilities for Coloring Properties of Random Hypergraphs;Problems of Information Transmission;2022-04

4. On the number of independent sets in uniform, regular, linear hypergraphs;European Journal of Combinatorics;2022-01

5. On the weak chromatic number of random hypergraphs;Discrete Applied Mathematics;2020-04

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