Alternating Hamiltonian cycles
Colour the edges of a complete graph with n vertices in such a way that no vertex is on more than k edges of the same colour. We prove that for every k there is a constant c ksuch that if n>c kthen there is a Hamiltonian cycle with adjacent edges having different colours. We prove a number of other results in the same vein and mention some unsolved problems. © 1976 The Weizmann Science Press of Israel.
Israel Journal of Mathematics
Bollobás, B., & Erdös, P. (1976). Alternating Hamiltonian cycles. Israel Journal of Mathematics, 23 (2), 126-131. https://doi.org/10.1007/BF02756791