@article{92c915baf12f49e88047c328d5cff6e3,
title = "Maximum size intersecting families of bounded minimum positive co-degree",
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.",
keywords = "Co-degree, Hypergraph, Intersecting",
author = "JOZSEF BALOGH and NATHAN LEMONS and CORY PALMER",
note = "Funding Information: \ast Received by the editors May 11, 2020; accepted for publication (in revised form) March 28, 2021; published electronically July 1, 2021. https://doi.org/10.1137/20M1336989 Funding: The first author was partially supported by NSF grant DMS-1764123 and by Arnold O. Beckman Research Award (UIUC) Campus Research Board 18132, a Simons Fellowship, and the Langan Scholar Fund (UIUC). The third author's research was supported by a grant from the Simons Foundation, 712036. \dagger Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA, and Moscow Institute of Physics and Technology (MIPT), Dolgoprudny, Moscow Region, 141701, Russian Federation (jobal@illinois.edu). \ddagger Theoretical Division, Los Alamos National Labratory, Los Alamos, NM 87545 USA (nlemons@ lanl.gov). \S Department of Mathematical Sciences, University of Montana, Missoula, MT 59801 USA (corypalmer@gmail.com). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2021",
doi = "10.1137/20M1336989",
language = "English (US)",
volume = "35",
pages = "1525--1535",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}