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.

Publication Title

Israel Journal of Mathematics