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An induced matching in a graph G is a matching such that its end vertices also induce a matching. A (1^, 2ᵏ) -packing edge-coloring of a graph G is a partition of its edge set into disjoint unions of matchings and k induced matchings. Gastineau and Togni (2019), as well as Hocquard, Lajou, and Luzar (2022), have conjectured that every subcubic graph is (1², 2⁴) -packing edge-colorable. In this paper, we confirm that their conjecture is true (for connected subcubic graphs with more than 70 vertices). Our result is sharp due to the existence of subcubic graphs that are not (1², 2³) -packing edge-colorable.
Liu et al. (Wed,) studied this question.
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