论文标题
矿石和pósa型条件，用于将$ 2 $ edged色的图形划分为单色周期
Ore- and Pósa-type conditions for partitioning $2$-edge-coloured graphs into monochromatic cycles
论文作者
论文摘要
在2019年，莱茨特证实了Balogh，Barát，Gerbner，Gyárfás和Sárközy的猜想，证明，每$ 2 $ 2 $ 2 $ edge的图形$ g $ g $ n $ n $ vertices上的$ n $ dertices上，至少$ 3N/4 $可以分配给两种单色颜色，以分配给两种单色不同的颜色。在这里，我们提出了$ g $的学位顺序较弱的条件，以保证这种分区并证明了大约版本。这类似于Barát和Sárközy实现的矿石型状况类似的概括。 艾伦（Allen），伯特（Böttcher），朗（Lang），斯科坎（Skokan）和斯坦因单色循环。
In 2019, Letzter confirmed a conjecture of Balogh, Barát, Gerbner, Gyárfás and Sárközy, proving that every large $2$-edge-coloured graph $G$ on $n$ vertices with minimum degree at least $3n/4$ can be partitioned into two monochromatic cycles of different colours. Here, we propose a weaker condition on the degree sequence of $G$ to also guarantee such a partition and prove an approximate version. This resembles a similar generalisation to an Ore-type condition achieved by Barát and Sárközy. Continuing work by Allen, Böttcher, Lang, Skokan and Stein, we also show that if $\operatorname{deg}(u) + \operatorname{deg}(v) \geq 4n/3 + o(n)$ holds for all non-adjacent vertices $u,v \in V(G)$, then all but $o(n)$ vertices can be partitioned into three monochromatic cycles.
