July 21 to August 2, 2019

Main Organizers:

• Ilkyoo Choi (Hankuk University of Foreign Studies)
• Suil O (SUNY-Korea)

Additional Organizers for summer of 2019:

• Ringi Kim (KAIST)
• Boram Park (Ajou University)

• KB Ingenium

Accomodation

• KB Ingenium

• July 21 (Sunday)
• 14:00 -- 16:00 registration & check in
• 16:00 -- 18:00 research session

July 22 (Monday)

• 10:00 -- 12:00 introduction and problem session (mandatory)
• 12:00 -- 14:00 lunch
• 14:00 -- 18:00 afternoon research session
• 18:00 -- banquet

July 23 (Tuesday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 15:00 lecture 1 (Seong-uk Nam): Generative Adversarial Newtroks And Its Applications

In recent years, the Neural Network have made great progress and being applied to various fields. In this talk, we introduce Generative Adversarial Networks (GAN), which is one of popular Neural Network models. The most part of this talk, we give a rigorous interpretation of the objective function of GAN, the two-player game between Generator and Discriminator. Some applications of GAN will be treated, including the competition "generative-dog-images" in Kaggle.

• 15:00 -- 18:00 afternoon research session
• 18:00 -- dinner

July 24 (Wednesday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 18:00 afternoon research session
• 18:00 -- dinner

July 25 (Thursday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 14:30 lecture 2 (Ilkyoo Choi): On flexibility of planar graphs

Given a graph G, a list assignment L is a function that assigns to each vertex v a list L(v) of available colors. An L-coloring is a proper coloring such that each vertex receives a color from its list. Given a graph G with a list assignment L, a request for G is a function r on a subset of V(G) such that r(v) is in L(v) for all v in dom(r). For e>0, a request r is e-satisfiable if there exists an L-coloring f of G such that f(v)=r(v) for at least e|dom(r)| vertices v in dom(r). A graph G is e-flexible if every request is e-satisfying. We survey results regarding flexibility of planar graphs.

• 14:30 -- 18:00 afternoon research session
• 18:00 -- dinner

July 26 (Friday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 18:00 afternoon research session
• 18:00 -- dinner

July27 (Saturday)

• 10:00 -- 14:00 Free
• 14:00 -- 18:00 research session

July28 (Sunday)

• 10:00 -- 14:00 Free
• 14:00 -- 18:00 research session

July 29 (Monday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 14:30 lecture 3 (Eun-Kyung Cho): Groups whose Cayley graphs are of class one

Vizing proved that the chromatic index $\chi'(G)$ is either $\Delta(G)$ or $\Delta(G)+1$. A graph $G$ is ``class one" if $\chi'(G)=\Delta(G)$, and of ``class two" otherwise. We would like to find all groups whose Cayley graphs are of class one. A Cayley graph is of class one if and only if it is $1$-factorizable. By this reasoning, our aim of finding all the groups whose Cayley graphs are of class one can be rephrased as finding all the groups whose Cayley graphs are $1$-factorizable. We know that all Cayley graphs of groups of odd order are not $1$-factorizable. In 1985, Strong proved that there is a $1$-factorization in every Cayley graph of $2$-groups, even order abelian groups, dihedral groups, and dicyclic groups. He also conjectured that all Cayley graphs of groups of even order are $1$-factorizable. We would like to check whether this is actually the case.

• 14:30 -- 18:00 afternoon research session
• 18:00 -- dinner

July 30 (Tuesday)

• 10:00 -- 18:00 research activity
• 18:00 -- banquet

July 31 (Wednesday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 14:30 lecture 4 (Ringi Kim): Decomposition of a planar graph into a forest and a 3-choosable subgraph

Recently, Grytczuk and Zhu proved that every planar graph G contains a matching M such that G-M is 4-choosable. In this talk, we show that every planar graph G contains a forest F such that G-E(F) is 3-choosable. We also show that a forest cannot be replaced by a subgraph of maximum degree at most 3 or a star forest. This is joint work with Seog-Jin Kim and Xuding Zhu.

• 14:30 -- 18:00 afternoon research session
• 18:00 -- dinner

August 1 (Thursday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 18:00 afternoon research session
• 18:00 -- dinner

August 2 (Friday)

• 10:00 -- 12:00 activity report (mandatory)
• 12:00 -- 14:00 lunch