SIAM Journal on Discrete Mathematics, Volume 35, Issue 2, Page 970-975, January 2021.
Balogh, Csaba, Jing, and Pluhár [Electron. J. Combin., 27 (2020)] recently determined the minimum degree threshold that ensures a 2-colored graph $G$ contains a Hamilton cycle of significant color bias (i.e., a Hamilton cycle that contains significantly more than half of its edges in one color). In this short note we extend this result, determining the corresponding threshold for $r$-colorings.

中文翻译：

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关于稠密图中颜色偏向哈密顿循环的注释

SIAM 离散数学杂志，第 35 卷，第 2 期，第 970-975 页，2021 年 1 月。Balogh
、Csaba、Jing 和 Pluhár [电子。J. Combin., 27 (2020)] 最近确定了最小度阈值，以确保 2 色图 $G$ 包含显着颜色偏差的哈密顿循环（即，汉密尔顿循环在一种颜色）。在这个简短的注释中，我们扩展了这个结果，确定了 $r$-colorings 的相应阈值。