On the $(1^2,2^4)$-packing edge-coloring of subcubic graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910347254824960 |
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| author | Liu, Xujun Yu, Gexin |
| author_facet | Liu, Xujun Yu, Gexin |
| contents | An induced matching in a graph $G$ is a matching such that its end vertices also induce a matching. A $(1^{\ell}, 2^k)$-packing edge-coloring of a graph $G$ is a partition of its edge set into disjoint unions of $\ell$ matchings and $k$ induced matchings. Gastineau and Togni (2019), as well as Hocquard, Lajou, and Lužar (2022), have conjectured that every subcubic graph is $(1^2,2^4)$-packing edge-colorable. In this paper, we confirm that their conjecture is true (for connected subcubic graphs with more than $70$ vertices). Our result is sharp due to the existence of subcubic graphs that are not $(1^2,2^3)$-packing edge-colorable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $(1^2,2^4)$-packing edge-coloring of subcubic graphs Liu, Xujun Yu, Gexin Combinatorics An induced matching in a graph $G$ is a matching such that its end vertices also induce a matching. A $(1^{\ell}, 2^k)$-packing edge-coloring of a graph $G$ is a partition of its edge set into disjoint unions of $\ell$ matchings and $k$ induced matchings. Gastineau and Togni (2019), as well as Hocquard, Lajou, and Lužar (2022), have conjectured that every subcubic graph is $(1^2,2^4)$-packing edge-colorable. In this paper, we confirm that their conjecture is true (for connected subcubic graphs with more than $70$ vertices). Our result is sharp due to the existence of subcubic graphs that are not $(1^2,2^3)$-packing edge-colorable. |
| title | On the $(1^2,2^4)$-packing edge-coloring of subcubic graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.18353 |