- Series
- Time
- Tuesday, March 7, 2023 - 3:45pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Daniel Cranston – Virginia Commonwealth University – dcranston@vcu.edu – https://www.people.vcu.edu/~dcranston/
- Organizer
- Tom Kelly

A \emph{list assignment} $L$ gives to each vertex $v$ in a graph $G$ a

list $L(v)$ of

allowable colors. An \emph{$L$-coloring} is a proper coloring $\varphi$ such that

$\varphi(v)\in L(v)$ for all $v\in V(G)$. An \emph{$L$-recoloring move} transforms

one $L$-coloring to another by changing the color of a single vertex. An

\emph{$L$-recoloring sequence} is a sequence of $L$-recoloring moves. We study

the problem of which hypotheses on $G$ and $L$ imply that for that every pair

$\varphi_1$ and $\varphi_2$ of $L$-colorings of $G$ there exists an $L$-recoloring

sequence that transforms $\varphi_1$ into $\varphi_2$. Further, we study bounds on

the length of a shortest such $L$-recoloring sequence.

We will begin with a survey of recoloring and list recoloring problems (no prior

background is assumed) and end with some recent results and compelling

conjectures. This is joint work with Stijn Cambie and Wouter Cames van

Batenburg.