Planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912170226221056 |
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| author | Jin, Ligang Kang, Yingli Zhu, Xuding |
| author_facet | Jin, Ligang Kang, Yingli Zhu, Xuding |
| contents | The concept of DP-coloring of graphs was introduced by Dvořák and Postle, and was used to prove that planar graphs without cycles of length from $4$ to $8$ are $3$-choosable. In the same paper, they proposed a more natural and stronger claim that such graphs are DP-$3$-colorable. This paper confirms that claim by proving a stronger result that planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19059 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable Jin, Ligang Kang, Yingli Zhu, Xuding Combinatorics 05C10, 05C15 The concept of DP-coloring of graphs was introduced by Dvořák and Postle, and was used to prove that planar graphs without cycles of length from $4$ to $8$ are $3$-choosable. In the same paper, they proposed a more natural and stronger claim that such graphs are DP-$3$-colorable. This paper confirms that claim by proving a stronger result that planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable. |
| title | Planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable |
| topic | Combinatorics 05C10, 05C15 |
| url | https://arxiv.org/abs/2412.19059 |