이상준

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  • Sang June Lee (이상준), On strong Sidon sets of integers

    IBS/KAIST Joint Discrete Math Seminar

    On strong Sidon sets of integers
    Sang June Lee
    Duksung Women’s University, Seoul
    2019/05/08 Wed 4:30PM-5:30PM (IBS, Room B232)
    Let N be the set of natural numbers. A set A⊂N is called a Sidon set if the sums a1+a2, with a1,a2∈S and a1≤a2, are distinct, or equivalently, if
    |(x+w)−(y+z)|≥1
    for every x,y,z,w∈S with x<y≤z<w. We define strong Sidon sets as follows:</p>

    For a constant α with 0≤α<1, a set S⊂N is called an α-strong Sidon set if
    |(x+w)−(y+z)|≥wα
    for every x,y,z,w∈S with x<y≤z<w.

    The motivation of strong Sidon sets is that a strong Sidon set generates many Sidon sets by altering each element a bit. This infers that a dense strong Sidon set will guarantee a dense Sidon set contained in a sparse random subset of N.

    In this talk, we are interested in how dense a strong Sidon set can be. This is joint work with Yoshiharu Kohayakawa, Carlos Gustavo Moreira and Vojtěch Rödl.

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  • 1st Korean Workshop on Graph Theory
    1st Korean Workshop on Graph Theory
    August 26-28, 2015
    KAIST  (E6-1 1501 & 3435)
    • 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:
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  • (ASARC seminar) Sang June Lee, Extremal results on combinatorial number theory

    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:</p>

    (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+.

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

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

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