Speaker: Xujun Liu (Xi'An Jiaotong-Liverpool University)
Title: Packing edge colorings of subcubic graphs
Abstract: A matching (induced matching) is a set of edges E such that each pair of edges in E has distance at least two (three). A (1l,2k)-packing edge-coloring of a graph G is a partition of its edge set into l matchings and k induced matchings. Gastineau and Togni showed there are subcubic graphs that are not (1,2,2,2,2,2,2)-packing (abbreviated to (1,26)-packing) edge-colorable and not (12,23)-packing edge-colorable. They also asked the question “whether every subcubic graph is (1,27)-packing edge-colorable?”. Very recently, Hocquard, Lajou, and Lu\v zar showed that every subcubic graph is (1,28)-packing edge-colorable and (12,25)-packing edge-colorable. They also conjectured that every subcubic graph is (1,27)-packing edge-colorable. Furthermore, Gastineau and Togni, as well as Hocquard, Lajou, and Lužar, have conjectured that every subcubic graph is (12,24)-packing edge-colorable.
We confirm both conjectures. This is based on a joint work with Santana and Short, and a joint work with Gexin Yu.
