Sequentially Swapping Colored Tokens on Graphs - Yamanaka, Katsuhisa; Demaine, Erik; Horiyama, Takashi; Kawamura, Akitoshi; Nakano, Shin-ichi; Okamoto, Yoshio; Saitoh, Toshiki; Suzuki, Akira; Uehara, Ryuhei; Uno, Takeaki (Journal of Graph Algorithms and Applications, 2019)
We consider a puzzle consisting of colored tokens on an n-vertex graph, where each token has a distinct starting vertex and a set of allowable target vertices for it to reach, and the only allowed transformation is to "sequentially" move the chosen token along a path of the graph by swapping it with other tokens on the path.