Abstract
Colour the edges of a complete graph withn vertices in such a way that no vertex is on more thank edges of the same colour. We prove that for everyk there is a constantc ksuch that ifn>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.
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References
D. E. Daykin,Graphs with cycles having adjacent lines different colours, to appear.
P. Erdös and T. Gallai,On maximal paths and circuits of graphs, Acta Math. Acad. Sci. Hungar.10, (1959), 337–356.
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Bollobás, B., Erdös, P. Alternating Hamiltonian cycles. Israel J. Math. 23, 126–131 (1976). https://doi.org/10.1007/BF02756791
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DOI: https://doi.org/10.1007/BF02756791