3‐colorability of 4‐regular hamiltonian graphs

On the model of the cycle‐plus‐triangles theorem, we consider the problem of 3‐colorability of those 4‐regular hamiltonian graphs for which the components of the edge‐complement of a given hamiltonian cycle are non‐selfcrossing cycles of constant length ≥ 4. We show that this problem is NP‐complete. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 125–140, 2003