Reconfiguration of Graph Colorings

For this thesis, we consider two $k$-colorings of a graph $G$ adjacent if one can recolor one into the other by changing the color of one vertex. The reconfiguration graph of a graph $G$ on $k$ colors $\mathcal{C}_{k}(G)$ is the graph for which the vertices are the $k$-colorings of $G$, and an edge is between two $k$-colorings if they are...