论文标题
半径，围环和最小程度
Radius, Girth and Minimum Degree
论文作者
论文摘要
给定$ n $顶点上的连接图$ g $，最低度$δ\ geq 2 $和girth至少$ g \ geq 4 $，此图可以有什么最大半径$ r $？在无三角形的情况下（$ g = 4 $）建立了$ r \ leq \ frac \ frac {n-2}δ+12 $，并指出添加剂常数的值，这很紧，这是紧密的。我们确定无三角形情况的确切值。对于更高的$ g $，鲜为人知。我们解决$ r $ $ g = 6,8,12 $的订单，并证明上订单的上订单甚至$ g $。最后，我们表明，证明对一般的$ g $的相应下限等同于围绕着围栏的猜想。
Given a connected graph $G$ on $n$ vertices, with minimum degree $δ\geq 2$ and girth at least $g \geq 4$, what is the maximum radius $r$ this graph can have? Erdős, Pach, Pollack and Tuza established in the triangle-free case ($g=4$) that $r \leq \frac{n-2}δ+12$, and noted that up to the value of the additive constant, this is tight. We determine the exact value for the triangle-free case. For higher $g$ little is known. We settle the order of $r$ for $g=6,8,12$ and prove an upper bound to the order for general even $g$. Finally, we show that proving the corresponding lower bound for general even $g$ is equivalent to the Erdős girth conjecture.
