A majority edge-coloring of a graph without pendant edges is a coloring of its edges such that, for every vertex v and every color \(\alpha \), there are at most as many edges incident to v colored with \(\alpha \) as with all other colors. We extend some known results for finite graphs to infinite graphs, also in the list setting. In particular, we prove that every infinite graph without pendant edges has a majority edge-coloring from lists of size 4. Another interesting result states that every infinite graph without vertices of finite odd degrees admits a majority edge-coloring from lists of size 2. As a consequence of our results, we prove that line graphs of any cardinality admit majority vertex-colorings from lists of size 2, thus confirming the Unfriendly Partition Conjecture for line graphs.

没有挂边的图形的多数边着色是对其边进行着色，使得对于每个顶点 v 和每种颜色 \（\alpha \），用 \（\alpha \） 着色的 v 的边最多与所有其他颜色一样多。我们将有限图的一些已知结果扩展到无限图，也是在 list 设置中。特别是，我们证明了每个没有挂边的无限图都具有大小为 4 的列表中的大多数边着色。另一个有趣的结果表明，每个没有有限奇数度顶点的无限图都允许大小为 2 的列表中的大多数边着色。作为我们结果的结果，我们证明了任何基数的折线图都接受大小为 2 的列表中的大多数顶点着色，从而证实了折线图的不友好划分猜想。