论文标题
大周围和小方向直径图
Large Girth and Small Oriented Diameter Graphs
论文作者
论文摘要
2015年，Dankelmann和Bau证明，对于每个无用的图形$ n $和最低度$δ$的每个无用图$ g $，最多有直径的方向，最多$ 11 \ frac {n} {δ+1}+9 $。在2016年，Surmacs将其减少到$ 7 \ frac {n} {δ+1}。$在本文中，我们考虑了图$ g $的围栏，并表明，对于任何$ \ varepsilon> 0 $，都有$（2G+\ varepsilon）的限制，$（2G+\ varepsilon）\ freac $ freac $ freac where n n} n} $ h（δ，g）$是多项式。让$ g = 3 $和$ \ varepsilon <1 $给出了Surmacs的结果。
In 2015, Dankelmann and Bau proved that for every bridgeless graph $G$ of order $n$ and minimum degree $δ$ there is an orientation of diameter at most $11\frac{n}{δ+1}+9$. In 2016, Surmacs reduced this bound to $7\frac{n}{δ+1}.$ In this paper, we consider the girth of a graph $g$ and show that for any $\varepsilon>0$ there is a bound of the form $(2g+\varepsilon)\frac{n}{h(δ,g)}+O(1)$, where $h(δ,g)$ is a polynomial. Letting $g=3$ and $\varepsilon<1$ gives an inprovement on the result by Surmacs.
