Chong Shangguan (上官冲), On the sparse hypergraph problem of Brown, Erdős and Sós

For fixed integers $r\ge 3, e\ge 3$, and $v\ge r+1$, let $f_r(n,v,e)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph in which the union of arbitrary $e$ distinct edges contains at least $v+1$ vertices. In 1973, Brown, Erdős and Sós initiated the study of the function $f_r(n,v,e)$ and they proved that $\Omega(n^{\frac{er-v}{e-1}})=f_r(n,v,e)=O(n^{\lceil\frac{er-v}{e-1}\rceil})$. We will survey the state-of-art results about the study of $f_r(n,er-(e-1)k+1,e)$ and $f_r(n,er-(e-1)k,e)$, where $r>k\ge 2$ and $e\ge 3$. Although these two functions have been extensively studied, many interesting questions remain open.

IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail:, Fax: +82-42-878-9209
Copyright © IBS 2018. All rights reserved.