Maximum size intersecting families of bounded minimum positive co-degree

JOZSEF BALOGH, NATHAN LEMONS, CORY PALMER

Research output: Contribution to journalArticlepeer-review

Abstract

Let H be an r-uniform hypergraph. The minimum positive co-degree of H , denoted by δ + r 1(H ), is the minimum k such that if S is an (r 1)-set contained in a hyperedge of H , then S is contained in at least k hyperedges of H . For r ≥ k fixed and n sufficiently large, we determine the maximum possible size of an intersecting r-uniform n-vertex hypergraph with minimum positive co-degree δ + r 1(H ) ≥ k and characterize the unique hypergraph attaining this maximum. This generalizes the Erdos-Ko-Rado theorem which corresponds to the case k = 1. Our proof is based on the delta-system method.

Original languageEnglish
Pages (from-to)1525-1535
Number of pages11
JournalSIAM Journal on Discrete Mathematics
Volume35
Issue number3
DOIs
StatePublished - 2021

Keywords

  • Co-degree
  • Hypergraph
  • Intersecting

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