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Zixiang Xu (徐子翔), On the degenerate Turán problems

October 4 Tuesday @ 4:30 PM - 5:30 PM KST

Room B332, IBS (기초과학연구원)

Speaker

Zixiang Xu (徐子翔)
IBS Extremal Combinatorics and Probability Group
https://drrichxu.github.io/Combinatorics/

For a graph $F$, the Turán number is the maximum number of edges in an $n$-vertex simple graph not containing $F$. The celebrated Erdős-Stone-Simonovits Theorem gives that \[ \text{ex}(n,F)=\bigg(1-\frac{1}{\chi(F)-1}+o(1)\bigg)\binom{n}{2},\] where $\chi(F)$ is the chromatic number of $H$. This theorem asymptotically solves the problem when $\chi(F)\geqslant 3$. In case of bipartite graphs $F$, not even the order of magnitude is known in general. In this talk, I will introduce some recent progress on Turán numbers of bipartite graphs and related generalizations and discuss several methods developed in recent years. Finally, I will introduce some interesting open problems on this topic.

Details

Date:
October 4 Tuesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Venue

Room B332
IBS (기초과학연구원)
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Organizer

Sang-il Oum (엄상일)
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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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