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Between proper and strong edge-colorings of subcubic graphsHocquard, Herve ; Lajou, Dimitri ; Lužar, BorutIn a proper edge-coloring the edges of every color form a matching. A matching is induced if the end-vertices of its edges induce a matching. A strong edge-coloring is an edge-coloring in which the ... edges of every color form an induced matching. We consider intermediate types of edge-colorings, where some of the colors are allowed to form matchings, and the remaining form induced matchings. Our research is motivated by the conjecture proposed in a recent paper on S-packing edge-colorings (N. Gastineau and O. Togni, On S-packing edge-colorings of cubic graphs, Discrete Appl. Math. 259 (2019)). We prove that every graph with maximum degree 3 can be decomposed into one matching and at most 8 induced matchings, and two matchings and at most 5 induced matchings. We also show that if a graph is in class I, the number of induced matchings can be decreased by one, hence confirming the conjecture for this class of graphs.Source: Combinatorial algorithms : proceedings (Str. 355-367)Type of material - conference contributionPublish date - 2020Language - englishCOBISS.SI-ID - 34012163
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Hocquard, Herve | |
Lajou, Dimitri | |
Lužar, Borut | 31670 |
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