A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. It is known that the list edge chromatic number Χ′ l ( G ) of any outer-1-planar graph G with maximum degree Δ( G ) ≥ 5 is exactly its maximum degree. In this paper, we prove Χ′ l ( G ) = Δ( G ) for outer-1-planar graphs G with Δ( G ) = 4 and with the crossing distance being at least 3.

中文翻译：

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列出外部 1 平面图的边缘着色

如果一个图可以在平面上绘制，使得所有顶点都在外面，并且每条边最多交叉一次，则该图是外 1 平面的。已知最大度Δ( G ) ≥ 5 的任何外1-平面图G 的列表边色数Χ′ l ( G ) 正是其最大度。在本文中，我们证明了 Χ′ l ( G ) = Δ( G ) 对于 Δ( G ) = 4 且交叉距离至少为 3 的外 1 平面图 G。