Department of Mathematics - Master Calendar

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Graph Theory and Combinatorics Seminar

Event Type
Department of Mathematics
Gregory 307
Apr 9, 2024   1:00 pm  
Xujun Liu (Xi'An Jiaotong-Liverpool University)
Peter Bradshaw
Originating Calendar
Combinatorics Research Area Calendar

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. 

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