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

November 17 Thursday @ 10:00 AM - 11:00 AM KST

Zoom ID: 224 221 2686 (ibsecopro)

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.

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Date:
November 17 Thursday
Time:
10:00 AM - 11:00 AM KST
Event Category:
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Venue

Zoom ID: 224 221 2686 (ibsecopro)

Organizer

Joonkyung Lee (이준경)
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: dimag@ibs.re.kr, Fax: +82-42-878-9209
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