[PAST EVENT] Mathematics Colloquium - Dan Cranston (VCU)

March 28, 2025
2pm - 3pm
Location
Jones Hall, Room 301
200 Ukrop Way
Williamsburg, VA 23185Map this location
Access & Features
  • Free food
  • Open to the public

Reconfiguration of Colorings and List Colorings

A \emph{proper $k$-coloring} of a graph $G$ assigns to each vertex $v$ a color $\alpha(v)$, with $\alpha(v)\in {1,\ldots,k}$ such that $\alpha(v) \ne \alpha(w)$ for every edge $vw$. (A \emph{list coloring} is similar, except that distinct vertices may have distinct lists of allowable colors.)

A \emph{recoloring step} in a graph $G$ for a coloring $\alpha$ recolors some vertex $v$ with a color allowable for $v$ that is not used by $\alpha$ on any neighbor of $v$, yielding a new proper coloring. Given proper colorings $\alpha$ and $\beta$ of $G$, we ask questions like: Can we transform $\alpha$ to $\beta$ by a sequence of recoloring steps? And: Over all $\alpha$ and $\beta$, what is the longest that a shortest sequence from $\alpha$ to $\beta$ can be?

In this talk we survey results on reconfiguration of colorings and list colorings. We end with a few conjectures.

Refreshments in lobby of Jones Hall at 1:30pm




Sponsored by: Mathematics

Contact

Gexin Yu