论文标题
将最低度$ 2N/3 + O（n）$的2边彩色图分配到三个单色周期中
Partitioning a 2-edge-coloured graph of minimum degree $2n/3 + o(n)$ into three monochromatic cycles
论文作者
论文摘要
Lehel在1970年代猜想，每个红色边缘色完整图都可以分为两个单色循环。 Bessy和Thomassé在2010年证实了这一点。但是，主机图$ G $不必完成。正如莱茨特（Letzter）最近显示的那样，要求$ g $具有至少$ 3N/4 $的最低学位，其中$ n $是$ g $的订单，这足以确认Balogh，Barát，Gerbner，Gyárfás和Sárközy的订单。该度条件渐近地很紧。 在这里，我们通过证明每$ n $ vertex图表的每条红色和蓝色边缘色至少至少$ 2N/3 + o（n）$，继续进行这一研究。这大约验证了Pokrovskiy的猜想，并且基本上很紧。
Lehel conjectured in the 1970s that every red and blue edge-coloured complete graph can be partitioned into two monochromatic cycles. This was confirmed in 2010 by Bessy and Thomassé. However, the host graph $G$ does not have to be complete. It it suffices to require that $G$ has minimum degree at least $3n/4$, where $n$ is the order of $G$, as was shown recently by Letzter, confirming a conjecture of Balogh, Barát, Gerbner, Gyárfás and Sárközy. This degree condition is asymptotically tight. Here we continue this line of research, by proving that for every red and blue edge-colouring of an $n$-vertex graph of minimum degree at least $2n/3 + o(n)$, there is a partition of the vertex set into three monochromatic cycles. This approximately verifies a conjecture of Pokrovskiy and is essentially tight.
