论文标题
对Bang-Jensen-Gutin猜想和Yeo定理的重审
A revisit to Bang-Jensen-Gutin conjecture and Yeo's theorem
论文作者
论文摘要
如果连续的边缘具有不同的颜色，则路径（周期）是正确色彩的。 1997年，Bang-Jensen和Gutin猜想在边缘色完整图中存在汉密尔顿路径的必要条件。这一猜想是2006年由Feng，Giesen，Guo，Gutin，Jensen和Rafley证实的，在Lo的Bollobás-Erdds猜想对汉密尔顿周期恰当的Bollobás-Erdős猜想的渐近证明中发挥了重要作用。在1997年，Yeo获得了边缘色图的结构表征，该图包含没有正确色彩的周期。该结果是边缘色图研究中的基本工具。在本文中，我们首先通过两个新颖的吸收诱饵来简短地证明了Bang-Jensen-Gutin的猜想。我们还证明了一个新的足够条件，可以使其存在适当的周期，然后从该结果中推断出Yeo的定理，并在边缘颜色图中推断出闭合概念。
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 Bollobás-Erdős' 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.
