A Short Proof that Every Claw-Free Cubic Graph is (1,1,2,2)-Packing Colorable
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912795326414848 |
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| author | Mortada, Maidoun Zein, Ayman El |
| author_facet | Mortada, Maidoun Zein, Ayman El |
| contents | It was recently proved that every claw-free cubic graph admits a (1, 1, 2, 2)-packing coloring--that is, its vertex set can be partitioned into two 1-packings and two 2-packings. This result was established by Brešar, Kuenzel, and Rall [Discrete Mathematics 348 (8) (2025), 114477]. In this paper, we provide a simpler and shorter proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Short Proof that Every Claw-Free Cubic Graph is (1,1,2,2)-Packing Colorable Mortada, Maidoun Zein, Ayman El Combinatorics It was recently proved that every claw-free cubic graph admits a (1, 1, 2, 2)-packing coloring--that is, its vertex set can be partitioned into two 1-packings and two 2-packings. This result was established by Brešar, Kuenzel, and Rall [Discrete Mathematics 348 (8) (2025), 114477]. In this paper, we provide a simpler and shorter proof. |
| title | A Short Proof that Every Claw-Free Cubic Graph is (1,1,2,2)-Packing Colorable |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.24001 |