A strong edge-coloring of a graph is a proper edge-coloring, in which the edges of every path of length 3 receive distinct colors; in other words, every pair of edges at distance at most 2 must be colored differently. The least number of colors needed for a strong edge-coloring of a graph is the strong chromatic index. We consider the list version of the coloring and prove that the list strong chromatic index of graphs with maximum degree 3 is at most 10. This bound is tight and improves the previous bound of 11 colors. We also consider the question whether the strong chromatic index and the list strong chromatic index always coincide. We answer it in negative by presenting an infinite family of graphs for which the two invariants differ. For the special case of the Petersen graph, we show that its list strong chromatic index equals 7, while its strong chromatic index is 5. Up to our best knowledge, this is the first known edge-coloring for which there are graphs with distinct values of the chromatic index and its list version. In relation to the above, we also initiate the study of the list version of the normal edge-coloring. A normal edge-coloring of a cubic graph is a proper edge-coloring, in which every edge is adjacent to edges colored with 4 colors or to edges colored with 2 colors. It is conjectured that 5 colors suffice for a normal edge-coloring of any bridgeless cubic graph which is equivalent to the Petersen Coloring Conjecture. Similarly to the strong edge-coloring, the list normal edge-coloring is much more restrictive and consequently for many graphs the list normal chromatic index is greater than the normal chromatic index. In particular, we show that there are cubic graphs with the list normal chromatic index at least 9, there are bridgeless cubic graphs with its value at least 8, and there are cyclically 4-edge-connected cubic graphs with value at least 7.

翻译：图的强边着色是一种正常边着色，其中每条长度为3的路径上的边必须被分配不同的颜色；换言之，距离不超过2的任意两条边必须被染以不同颜色。实现图强边着色所需的最少颜色数称为强色指数。本文研究该着色问题的列表版本，并证明最大度为3的图的列表强色指数至多为10。该界限是紧的，且改进了先前11种颜色的界限。我们还探讨强色指数与列表强色指数是否始终相等的问题，通过构造一个无限图族证明二者存在差异，从而给出否定回答。特别针对Petersen图，我们证明其列表强色指数等于7，而其强色指数为5。据我们所知，这是首次在边着色问题中发现色指数与其列表版本取值不同的图例。基于上述研究，我们同时开创性地探讨了正规边着色的列表版本。立方图的正规边着色是一种正常边着色，其中每条边要么邻接4种颜色的边，要么邻接2种颜色的边。现有猜想认为5种颜色足以实现任意无桥立方图的正规边着色，该猜想等价于Petersen着色猜想。与强边着色类似，列表正规边着色具有更强的限制性，因此对许多图而言，其列表正规色指数大于正规色指数。具体而言，我们证明存在列表正规色指数至少为9的立方图，存在列表正规色指数至少为8的无桥立方图，以及存在列表正规色指数至少为7的循环4边连通立方图。