论文标题
关于最低度图的单色组件的注释
A note about monochromatic components in graphs of large minimum degree
论文作者
论文摘要
对于所有积极整数$ r \ geq 3 $和$ n $，以使$ r^2-r $划分$ n $和订单$ r $的仿射平面，我们构造了一个$ r $ - 边缘的彩色图，最低度$（1- \ frac {r-2} {r-2} {r^2-r} {r^2-r}）{r^2-r}）n-2 $ and $ components n $ components n n n $ nsements n n n n n n n n n of $ frac。这概括了Guggiari和Scott的一个例子，并独立于Rahimi，以$ R = 3 $，因此反驳了Gyárfás和Sárközy对所有整数的猜想。
For all positive integers $r\geq 3$ and $n$ such that $r^2-r$ divides $n$ and an affine plane of order $r$ exists, we construct an $r$-edge colored graph with minimum degree $(1-\frac{r-2}{r^2-r})n-2$ such that the largest monochromatic component has order less than $\frac{n}{r-1}$. This generalizes an example of Guggiari and Scott and, independently, Rahimi for $r=3$ and thus disproves a conjecture of Gyárfás and Sárközy for all integers $r\geq 3$ such that an affine plane of order $r$ exists.
