论文标题
用超级分配挖掘至少4个
Partitioning digraphs with outdegree at least 4
论文作者
论文摘要
斯科特问了确定$ c_d $的问题，以便如果$ d $是$ m $ arcs的挖掘物和最少的超级$ d \ ge 2 $ 2 $，则$ v（d）$具有分区$ v_1，v_2 $，以便$ \ min \ min \ min \ min \ weft \ left \ left \ weft \ { $ e（v_1，v_2）$（分别分别为$ e（v_2，v_1）$）是弧线的数量，从$ v_1 $到$ v_2 $（分别为$ v_2 $从$ v_2 $到$ v_1 $）。 Lee，Loh和Sudakov表明$ C_2 = 1/6+O（1）$和$ C_3 = 1/5+O（1）$，并推测$ C_D = \ frac {d-1} {D-1} {2（2DD-1）}+o（1）+o（1）$（对于$ d \ ge 4 $。在本文中，我们显示$ C_4 = 3/14+O（1）$，并证明$ D \ GE 5 $的部分结果。
Scott asked the question of determining $c_d$ such that if $D$ is a digraph with $m$ arcs and minimum outdegree $d\ge 2$ then $V(D)$ has a partition $V_1, V_2$ such that $\min\left\{e(V_1,V_2),e(V_2, V_1)\right\}\geq c_dm$, where $e(V_1,V_2)$ (respectively, $e(V_2,V_1)$) is the number of arcs from $V_1$ to $V_2$ (respectively, from $V_2$ to $V_1$). Lee, Loh, and Sudakov showed that $c_2=1/6+o(1)$ and $c_3=1/5+o(1)$, and conjectured that $c_d= \frac{d-1}{2(2d-1)}+o(1)$ for $d\ge 4$. In this paper, we show $c_4=3/14+o(1)$ and prove some partial results for $d\ge 5$.
