Connectedness and Cycle Spaces of Friends-and-Strangers Graphs

Colin Defant, David Dong, Alan Lee +1

If $X=(V(X),E(X))$ and $Y=(V(Y),E(Y))$ are $n$-vertex graphs, then their friends-and-strangers graph $\mathsf{FS}(X,Y)$ is the graph whose vertices are the bijections from $V(X)$ t…