论文标题
在列表着色上，与完整的图形和设置系统交叉点的分离
On List Coloring with Separation of the Complete Graph and Set System Intersections
论文作者
论文摘要
我们考虑以下具有分离问题的列表颜色：给定图形$ g $和整数$ a，b $，找到最大的整数$ c $，以便对于任何列表任务$ l $ g $ a $ g $带有$ | l（v）| = a $ for vertex $ v $ v $ and $ | l（u | l（u cap l（v）$ c $ $ c $ $ c $ $ c $ $ c $ c $ a n exts | $ g $的顶点的整数使得$φ（u）\ subset l（u）$和$ |φ（v）| = b $用于任何顶点$ u $和$φ（u）\capφ（v）= \ emptyset $对于任何边缘$ uv $。这样的$ c $的值称为$（g，a，b）$的分离数。使用一组列表的特殊分区，我们为其获得了Poincaré的Crible的改进版本，我们确定了完整的图形$ k_n $的分离数，对于$ a，b $和$ n $的某些值，并证明了其余值的界限。
We consider the following list coloring with separation problem: Given a graph $G$ and integers $a,b$, find the largest integer $c$ such that for any list assignment $L$ of $G$ with $|L(v)|= a$ for any vertex $v$ and $|L(u)\cap L(v)|\le c$ for any edge $uv$ of $G$, there exists an assignment $φ$ of sets of integers to the vertices of $G$ such that $φ(u)\subset L(u)$ and $|φ(v)|=b$ for any vertex $u$ and $φ(u)\cap φ(v)=\emptyset$ for any edge $uv$. Such a value of $c$ is called the separation number of $(G,a,b)$. Using a special partition of a set of lists for which we obtain an improved version of Poincaré's crible, we determine the separation number of the complete graph $K_n$ for some values of $a,b$ and $n$, and prove bounds for the remaining values.
