A Proof to Bang‐Jensen, Havet and Yeo's Conjecture on the Hamiltonian Cycles Avoiding Prescribed Arcs in Semicomplete Digraphs
Ruijuan Li, Yaoxiang Di, Ruiping Zhang, Xinhong Zhang · Journal of Graph Theory · 2025
ABSTRACT In 2023, Bang‐Jensen, Havet and Yeo [J. Graph Theory 102 (2023) 578‐606] conjectured that every ‐strong semicomplete digraph contains a hamiltonian cycle avoiding any prescribed set of arcs, which was inspired by the result of Fraisse and Thomassen that, every ‐strong tournament contains a hamiltonian cycle avoiding any prescribed set of arcs. In this paper, we prove the conjecture.