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An edge‐colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang‐Jensen and G. Gutin conjectured that an edge‐colored complete graph G has a properly colored Hamilton path if and only if G has a spanning subgraph consisting of a properly colored path C 0 and a (possibly empty) collection of properly colored cycles C 1 , C 2 ,…, C d such that V (Cᵢ) ∩ V(Cⱼ) =∅ provided 0 ≤ i < j ≤ d . We prove this conjecture.
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Feng et al. (2006) studied this question.
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