Coloring Graphs With No Totally Odd Clique Immersion

Fuente: arXiv
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Autor principal: McFarland, Caleb
Formato: Preprint
Publicado: 2025
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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