论文标题
在足够的条件下，平面图是5富集的
On sufficient conditions for planar graphs to be 5-flexible
论文作者
论文摘要
在本文中，我们研究了两个平面图类的灵活性$ \ MATHCAL {H} _1 $，$ \ MATHCAL {H} _2 $，其中$ \ Mathcal {H} _1 $，$ \ Mathcal {h} _2 _2 _2 $表示所有霍珀 - 福里平面图和房屋图形图的集合。令$ g $是带有列表分配$ l $的平面图。假设给出某些顶点的首选颜色。我们证明，如果在\ Mathcal {h} _1 $或$ g \ in \ Mathcal {h} _2 $中，以使所有列表的大小至少$ 5 $，则存在$ l $ coloring尊重至少持续的偏好分数。
In this paper, we study the flexibility of two planar graph classes $\mathcal{H}_1$, $\mathcal{H}_2$, where $\mathcal{H}_1$, $\mathcal{H}_2$ denote the set of all hopper-free planar graphs and house-free planar graphs, respectively. Let $G$ be a planar graph with a list assignment $L$. Suppose a preferred color is given for some of the vertices. We prove that if $G\in \mathcal{H}_1$ or $G\in \mathcal{H}_2$ such that all lists have size at least $5$, then there exists an $L$-coloring respecting at least a constant fraction of the preferences.
