Coloring Graphs With No Totally Odd Clique Immersion
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916909127041024 |
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| author | McFarland, Caleb |
| author_facet | McFarland, Caleb |
| contents | We prove that graphs that do not contain a totally odd immersion of $K_t$ are $\mathcal{O}(t)$-colorable. In particular, we show that any graph with no totally odd immersion of $K_t$ is the union of a bipartite graph and a graph which forbids an immersion of $K_{\mathcal{O}(t)}$. Our results are algorithmic, and we give a fixed-parameter tractable algorithm (in $t$) to find such a decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coloring Graphs With No Totally Odd Clique Immersion McFarland, Caleb Combinatorics Discrete Mathematics 05C15, 05C83 G.2.2 We prove that graphs that do not contain a totally odd immersion of $K_t$ are $\mathcal{O}(t)$-colorable. In particular, we show that any graph with no totally odd immersion of $K_t$ is the union of a bipartite graph and a graph which forbids an immersion of $K_{\mathcal{O}(t)}$. Our results are algorithmic, and we give a fixed-parameter tractable algorithm (in $t$) to find such a decomposition. |
| title | Coloring Graphs With No Totally Odd Clique Immersion |
| topic | Combinatorics Discrete Mathematics 05C15, 05C83 G.2.2 |
| url | https://arxiv.org/abs/2508.08119 |