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# Ilkyoo Choi (최일규), Flexibility of Planar Graphs

## Tuesday, July 21, 2020 @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

### Speaker

Ilkyoo Choi (최일규)
Department of Mathematics, Hankuk University of Foreign Studies

Oftentimes in chromatic graph theory, precoloring techniques are utilized in order to obtain the desired coloring result. For example, Thomassen’s proof for 5-choosability of planar graphs actually shows that two adjacent vertices on the same face can be precolored. In this vein, we investigate a precoloring extension problem formalized by Dvorak, Norin, and Postle named flexibility. Given a list assignment $L$ on a graph $G$, an $L$-request is a function on a subset $S$ of the vertices that indicates a preferred color in $L(v)$ for each vertex $v\in S$. A graph $G$ is $\varepsilon$-flexible for list size $k$ if given a $k$-list assignment $L$ and an $L$-request, there is an $L$-coloring of $G$ satisfying an $\varepsilon$-fraction of the requests in $S$. We survey known results regarding this new concept, and prove some new results regarding flexibility of planar graphs.

## Details

Date:
Tuesday, July 21, 2020
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:
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Room B232
IBS (기초과학연구원)

## Organizer

Sang-il Oum (엄상일)
View Organizer Website
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