论文标题
Dirac定理的定向差异版本
An oriented discrepancy version of Dirac's theorem
论文作者
论文摘要
近年来，由ERDS发起的图形差异问题的研究引起了人们的重新关注。通常，给定$ 2 $边缘的图形$ g $，一个人有兴趣嵌入$ g $中的图$ h $的副本具有较大的差异（即，$ h $的副本大大包含其一半以上其边缘的一半以一种颜色）。 Gishboliner，Krivelevich和Michaeli是由这一研究的动机，被认为是汉密尔顿周期的图形差异。特别是，他们猜想了Dirac定理的以下概括：如果$ g $是$ n \ geq3 $顶点的定向图，则具有$δ（g）\ geq n/2 $，则$ g $包含一个至少$δ（g）$ edges向前向前的汉密尔顿周期。在本文中，我们为这个猜想提供了完整的解决方案。
The study of graph discrepancy problems, initiated by Erdős in the 1960s, has received renewed attention in recent years. In general, given a $2$-edge-coloured graph $G$, one is interested in embedding a copy of a graph $H$ in $G$ with large discrepancy (i.e. the copy of $H$ contains significantly more than half of its edges in one colour). Motivated by this line of research, Gishboliner, Krivelevich and Michaeli considered an oriented version of graph discrepancy for Hamilton cycles. In particular, they conjectured the following generalization of Dirac's theorem: if $G$ is an oriented graph on $n\geq3$ vertices with $δ(G)\geq n/2$, then $G$ contains a Hamilton cycle with at least $δ(G)$ edges pointing forward. In this paper, we present a full resolution to this conjecture.
