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- W4285038561 abstract "A path (cycle) is properly-colored if consecutive edges are of distinct colors. In 1997, Bang-Jensen and Gutin conjectured a necessary and sufficient condition for the existence of a Hamilton path in an edge-colored complete graph. This conjecture, confirmed by Feng, Giesen, Guo, Gutin, Jensen and Rafley in 2006, was laterly playing an important role in Lo's asymptotical proof of Bollob'as-ErdH{o}s' conjecture on properly-colored Hamilton cycles. In 1997, Yeo obtained a structural characterization of edge-colored graphs that containing no properly colored cycles. This result is a fundamental tool in the study of edge-colored graphs. In this paper, we first give a much shorter proof of the Bang-Jensen-Gutin Conjecture by two novel absorbing lemmas. We also prove a new sufficient condition for the existence of a properly-colored cycle and then deduce Yeo's theorem from this result and a closure concept in edge-colored graphs." @default.
- W4285038561 created "2022-07-12" @default.
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- W4285038561 date "2022-07-08" @default.
- W4285038561 modified "2023-09-25" @default.
- W4285038561 title "A revisit to Bang-Jensen-Gutin conjecture and Yeo's theorem" @default.
- W4285038561 doi "https://doi.org/10.48550/arxiv.2207.03793" @default.
- W4285038561 hasPublicationYear "2022" @default.
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