Linear colorings of graphs
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917332021936128 |
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| author | Hilaire, Claire Krnc, Matjaž Milanič, Martin Raymond, Jean-Florent |
| author_facet | Hilaire, Claire Krnc, Matjaž Milanič, Martin Raymond, Jean-Florent |
| contents | Motivated by algorithmic applications, Kun, O'Brien, Pilipczuk, and Sullivan introduced the parameter linear chromatic number as a relaxation of treedepth and proved that the two parameters are polynomially related. They conjectured that treedepth could be bounded from above by twice the linear chromatic number.
In this paper we investigate the properties of linear chromatic number and provide improved bounds in several graph classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear colorings of graphs Hilaire, Claire Krnc, Matjaž Milanič, Martin Raymond, Jean-Florent Combinatorics Discrete Mathematics Motivated by algorithmic applications, Kun, O'Brien, Pilipczuk, and Sullivan introduced the parameter linear chromatic number as a relaxation of treedepth and proved that the two parameters are polynomially related. They conjectured that treedepth could be bounded from above by twice the linear chromatic number. In this paper we investigate the properties of linear chromatic number and provide improved bounds in several graph classes. |
| title | Linear colorings of graphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2505.02768 |