Posts Tagged ‘이상준’

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:

(ASARC seminar) Sang June Lee, Extremal results on combinatorial number theory

Thursday, March 14th, 2013

FYI (ASARC seminar)

Extremal results on combinatorial number theory
Sang June Lee
ASARC, KAIST
2013/03/15 Thu 5PM-6PM
In this talk we deal with extremal results on combinatorial number theory. A typical problem is as follows. We fix a family of linear equations (for example, a+b=2c or a+b=c+d). Then we want to estimate the maximum size of subsets with no solution of the given equations in {1,2,…,n} or a random subset of {1,2,…,n} of size m < n. We consider two important examples:

(1) Sets which contain no arithmetic progression of a fixed size

(2) Sidon sets (without solutions of a+b=c+d)

The first example is about the results of Roth in 1953 and Szemeredi in 1975, and the recent results by Schacht in 2009+, and Conlon-Gowers in 2010+.

Next, the second example is about the results by Erdős, Turán, Chowla, Singer in 1940s and the results by Kohayakawa, Lee, Rödl, and Samotij in 2012+.

Sang June Lee (이상준), Dynamic coloring and list dynamic coloring of planar graphs

Tuesday, June 12th, 2012
Dynamic coloring and list dynamic coloring of planar graphs
Sang June Lee (이상준)
Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia, USA
2012/06/27 Wed 4PM-5PM

A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A dynamic k-coloring of a graph is a dynamic coloring with k colors. Note that the gap χd(G) – χ(G) could be arbitrarily large for some graphs. An interesting problem is to study which graphs have small values of χd(G) – χ(G).
One of the most interesting problems about dynamic chromatic numbers is to find upper bounds of χd(G)$ for planar graphs G. Lin and Zhao (2010) and Fan, Lai, and Chen (recently) showed that for every planar graph G, we have χd(G)≤5, and it was conjectured that χd(G)≤4 if G is a planar graph other than C5. (Note that χd(C5)=5.)
As a partial answer, Meng, Miao, Su, and Li (2006) showed that the dynamic chromatic number of Pseudo-Halin graphs, which are planar graphs, are at most 4, and Kim and Park (2011) showed that χd(G)≤4 if G is a planar graph with girth at least 7.
In this talk we settle the above conjecture that χd≤4 if G is a planar graph other than C5. We also study the corresponding list coloring called a list dynamic coloring.
This is joint work with Seog-Jin Kim and Won-Jin Park.

Sangjune Lee (이상준), The maximum size of a Sidon set contained in a sparse random set of integers

Monday, May 23rd, 2011
The maximum size of a Sidon set contained in a sparse random set of integers
Sangjune Lee (이상준)
Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia, USA
2011/06/09 Thu 4PM-5PM

A set A of integers is a Sidon set if all the sums a1+a2, with a1≤a2 and a1, a2∈A, are distinct. In the 1940s, Chowla, Erdős and Turán showed that the maximum possible size of a Sidon set contained in [n]={0,1,…,n-1} is √n (1+o(1)). We study Sidon sets contained in sparse random sets of integers, replacing the ‘dense environment’ [n] by a sparse, random subset R of [n].

Let R=[n]m be a uniformly chosen, random m-element subset of [n]. Let F([n]m)=max {|S| : S⊆[n]m Sidon}. An abridged version of our results states as follows. Fix a constant 0≤a≤1 and suppose m=m(n)=(1+o(1))na. Then there is a constant b=b(a) for which F([n]m)=nb+o(1) almost surely. The function b=b(a) is a continuous, piecewise linear function of a, not differentiable at two points: a=1/3 and a=2/3; between those two points, the function b=b(a) is constant. This is joint work with Yoshiharu Kohayakawa and Vojtech Rödl.