Hahn's nonincreasing-distance conjecture for cop-win graphs
Let be an undirected cop-win graph, and consider optimal play, meaning that the cop minimizes capture time while the robber maximizes it. Hahn's conjecture. The distance between the cop and robber does not increase in consecutive rounds in optimal play.
This conjecture was posed by Hahn and published in B+13. It was refuted there.
References
Primary source
Devvrit Khatri, Natasha Komarov, Aaron Krim-Yee, Nithish Kumar, Ben Seamone, Virgélot Virgile and AnQi Xu, “A study of cops and robbers in oriented graphs”, arXiv:1811.06155 (2019).
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