Proper colorings of a graph in linear time using a number of colors linear in the maximum degree of the graph
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917177844563968 |
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| author | Bhandari, Kritika Huber, Mark |
| author_facet | Bhandari, Kritika Huber, Mark |
| contents | A new algorithm for exactly sampling from the set of proper colorings of a graph is presented. This is the first such algorithm that has an expected running time that is guaranteed to be linear in the size of a graph with maximum degree \( Δ\) when the number of colors is greater than \( 3.637 Δ+ 1\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proper colorings of a graph in linear time using a number of colors linear in the maximum degree of the graph Bhandari, Kritika Huber, Mark Probability Computational Complexity Data Structures and Algorithms 60-08, 05C85 F.2.2; G.3; G.2.2 A new algorithm for exactly sampling from the set of proper colorings of a graph is presented. This is the first such algorithm that has an expected running time that is guaranteed to be linear in the size of a graph with maximum degree \( Δ\) when the number of colors is greater than \( 3.637 Δ+ 1\). |
| title | Proper colorings of a graph in linear time using a number of colors linear in the maximum degree of the graph |
| topic | Probability Computational Complexity Data Structures and Algorithms 60-08, 05C85 F.2.2; G.3; G.2.2 |
| url | https://arxiv.org/abs/2512.24522 |