Between proper and strong edge‐colorings of subcubic graphs

In a proper edge-coloring the edges of every color form matching. A matching is induced if end-vertices its induce strong an in which We consider intermediate types edge-colorings, where some colors are allowed to matchings, and remaining matchings. Our research motivated by conjecture proposed recent paper Gastineau Togni on S-packing edge-colorings (On cubic graphs, Discrete Appl. Math. 259 (2019), 63-75) asserting that allowing three additional one able save color. prove graph with maximum degree 3 can be decomposed into at most 8 two matchings 5 also show class I, number decreased one, hence confirming above-mentioned for I graphs.