Posts Tagged ‘이준경’

Joonkyung Lee (이준경), The extremal number of subdivisions

Thursday, September 13th, 2018
The extremal number of subdivisions
Joonkyung Lee (이준경)
Universität Hamburg, Hamburg, Germany
2018/9/17 Monday 5PM
One of the cornerstones of extremal graph theory is a result of Füredi, later reproved and given due prominence by Alon, Krivelevich and Sudakov, saying that if H is a bipartite graph with maximum degree r on one side, then there is a constant C such that every graph with n vertices and C n2 – 1/r edges contains a copy of H. This result is tight up to the constant when H contains a copy of Kr,s with s sufficiently large in terms of r. We conjecture that this is essentially the only situation in which Füredi’s result can be tight and prove this conjecture for r = 2. More precisely, we show that if H is a C4-free bipartite graph with maximum degree 2 on one side, then there are positive constants C and δ such that every graph with n vertices and C n3/2 – δ edges contains a copy of H. This answers a question by Erdős from 1988. The proof relies on a novel variant of the dependent random choice technique which may be of independent interest. This is joint work with David Conlon.

Joonkyung Lee (이준경), Counting tree-like graphs in locally dense graphs

Monday, January 1st, 2018
Counting tree-like graphs in locally dense graphs
Joonkyung Lee (이준경)
Mathematical Institute, University of Oxford, Oxford, UK
2018/1/8 Mon 4PM-5PM
We prove that a class of graphs obtained by gluing complete multipartite graphs in a tree-like way satisfies a conjecture of Kohayakawa, Nagle, Rödl, and Schacht on random-like counts for small graphs in locally dense graphs. This implies an approximate version of the conjecture for graphs with bounded tree-width. We also prove an analogous result for odd cycles instead of complete multipartite graphs.
The proof uses a general information theoretic method to prove graph homomorphism inequalities for tree-like structured graphs, which may be of independent interest.

1st Korean Workshop on Graph Theory

Tuesday, July 28th, 2015
1st Korean Workshop on Graph Theory
August 26-28, 2015
KAIST  (E6-1 1501 & 3435)
http://home.kias.re.kr/MKG/h/KWGT2015/
  • Program Book
  • Currently, we are planning to have talks in KOREAN.
  • Students/postdocs may get the support for the accommodation. (Hotel Interciti)
  • Others may contact us if you wish to book a hotel at a pre-negotiated price. Please see the website.
  • We may or may not have contributed talks. If you want, please contact us.
  • PLEASE REGISTER UNTIL AUGUST 16.
Location: KAIST
  • Room 1501 of E6-1 (August 26, 27)
  • Room 3435 of E6-1 (August 28)
Invited Speakers:
Organizers:

Joonkyung Lee, Some Advances in Sidorenko’s Conjecture

Tuesday, August 26th, 2014
Some Advances in Sidorenko’s Conjecture
Joonkyung Lee
University of Oxford, UK
2014/09/04 *Thursday* 4PM-5PM
Room 1409
Sidorenko’s conjecture states that for every bipartite graph \(H\) on \(\{1,\cdots,k\}\)
\begin{eqnarray*}
\int \prod_{(i,j)\in E(H)} h(x_i, y_j) d\mu^{|V(H)|}
\ge \left( \int h(x,y) \,d\mu^2 \right)^{|E(H)|}
\end{eqnarray*}
holds, where \(\mu\) is the Lebesgue measure on \([0,1]\) and \(h\) is a bounded, non-negative, symmetric, measurable function on \([0,1]^2\). An equivalent discrete form of the conjecture is that the number of homomorphisms from a bipartite graph \(H\) to a graph \(G\) is asymptotically at least the expected number of homomorphisms from \(H\) to the Erdos-Renyi random graph with the same expected edge density as \(G\). In this talk, we will give an overview on known results and new approaches to attack Sidorenko’s conjecture.
This is a joint work with Jeong Han Kim and Choongbum Lee.