A topological proof of the Hell-Ne\vset\vril dichotomy
<|reference_start|>A topological proof of the Hell-Ne\vset\vril dichotomy: We provide a new proof of a theorem of Hell and Ne\v{s}et\v{r}il [J. Comb. Theory B, 48(1):92-110, 1990] using tools from topological combinatorics based on ideas of Lov\'asz [J. Comb. Theory, Ser. A, 25(3):319-324, 1978]. The Hell-Ne\v{s}et\v{r}il Theorem provides a dichotomy of the graph homomorphism problem. It states that deciding whether there is a graph homomorphism from a given graph to a fixed graph $H$ is in P if $H$ is bipartite (or contains a self-loop), and is NP-complete otherwise. In our proof we combine topological combinatorics with the algebraic approach to constraint satisfaction problem.<|reference_end|>
@article{meyer2024a,
    title={A topological proof of the Hell-Ne\v{s}et\v{r}il dichotomy},
    author={Sebastian Meyer and Jakub Oprv{s}al},
    journal={arXiv preprint arXiv:2409.12627},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12627},
    primaryClass={cs.CC math.AT math.CO}
}