On Wegner's 8-Coloring Theorem for Planar Graphs of Maximum Degree Three
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917076287881216 |
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| author | Elvin, Gabriel Fejzić, Hajrudin Kim, Youngsu |
| author_facet | Elvin, Gabriel Fejzić, Hajrudin Kim, Youngsu |
| contents | We provide a simplified proof of the following special case of Wegner's conjecture: every planar graph of maximum degree at most three admits a distance-2 coloring with at most eight colors. Our main contribution is significant simplification of the most technically challenging part of Wegner's proof: the case involving the removal of a 5-cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Wegner's 8-Coloring Theorem for Planar Graphs of Maximum Degree Three Elvin, Gabriel Fejzić, Hajrudin Kim, Youngsu Combinatorics We provide a simplified proof of the following special case of Wegner's conjecture: every planar graph of maximum degree at most three admits a distance-2 coloring with at most eight colors. Our main contribution is significant simplification of the most technically challenging part of Wegner's proof: the case involving the removal of a 5-cycle. |
| title | On Wegner's 8-Coloring Theorem for Planar Graphs of Maximum Degree Three |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.09391 |