On S-packing edge-colorings of graphs with small edge weight

Highlights：

• We confirm the question in affirmative with a stronger way. It is shown that for any graph G (not necessarily subcubic bipartite) with w(e)≤5 is (1,24)-packing edge-colorable.

• We also prove that every graph G with w(e)≤6 is (1,28)-packing edge-colorable.

• we prove that if G is cubic graph, then it has a (1,320)-packing edge-coloring and a (1,447)-packing edge-coloring. Furthermore, if G is 3-edge-colorable, then it has a (1,318)-packing edge-coloring and a (1,442)-packing edge-coloring. These strengthen results of Gastineau and Togni (On S-packing edge-colorings of cubic graphs, Discrete Appl. Math. 259 (2019) 63–75).

摘要

•We confirm the question in affirmative with a stronger way. It is shown that for any graph G (not necessarily subcubic bipartite) with w(e)≤5 is (1,24)-packing edge-colorable.•We also prove that every graph G with w(e)≤6 is (1,28)-packing edge-colorable.•we prove that if G is cubic graph, then it has a (1,320)-packing edge-coloring and a (1,447)-packing edge-coloring. Furthermore, if G is 3-edge-colorable, then it has a (1,318)-packing edge-coloring and a (1,442)-packing edge-coloring. These strengthen results of Gastineau and Togni (On S-packing edge-colorings of cubic graphs, Discrete Appl. Math. 259 (2019) 63–75).

论文评审过程：Received 5 July 2021, Revised 23 November 2021, Accepted 26 November 2021, Available online 9 December 2021, Version of Record 9 December 2021.