A note on alternating cycles in edge-coloured graphs (Q1354729)

\textit{J. W. Grossman} and \textit{R. Häggkvist} [J. Comb. Theory, Ser. B 34, 77-81 (1983; Zbl 0491.05039)] gave a sufficient condition for a 2-edge-coloured graph to have an alternating cycle (i.e. a cycle with no two consecutive edges of the same colour). In the paper, this sufficient condition is extended to edge-coloured graphs with any number of colours. This allows to verify in polynomial time if an edge-coloured graph has an alternating cycle. For more information on alternating paths and cycles, see \textit{J. Bang-Jensen} and \textit{G. Gutin} [Alternating cycles and paths in edge-coloured multigraphs: A survey, Discrete Math. 165-166, 39-60 (1997)].