최일규

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 …

A graph $G$ is (list, DP) $k$-critical if the (list, DP) chromatic number is $k$ but for every proper subgraph $G'$ of $G$, the (list, DP) chromatic number of $G'$ is less than $k$. For $k\geq 4$, we show a bound on the minimum number of edges in a DP $k$-critical graph, and our bound …