On July 21, 2020, Ilkyoo Choi (최일규) from Hankuk University of Foreign Studies gave a talk on the flexibility of planar graphs, a concept related to extending a a precoloring at the Discrete Math Seminar. The title of his talk was “Flexibility of Planar Graphs“.

## Ilkyoo Choi (최일규), Flexibility of Planar Graphs

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.