Two-block cycles and chromatic number of Hamiltonian digraphs

Ruilin Zheng, Junying Lu, Xiaolin Wang +1

The paper proves that any Hamiltonian digraph avoiding a two‑block cycle C(k,ℓ) has chromatic number at most k + ℓ − 1 for k + ℓ ≥ 6, confirming a conjectured bound.