Crossing lemmas for $k$-systems of arcs
<|reference_start|>Crossing lemmas for $k$-systems of arcs: We show a generalization of the crossing lemma for multi-graphs drawn on orientable surfaces in which pairs of edges are assumed to be drawn by non-homotopic simple arcs which pairwise cross at most $k$ times.<|reference_end|>
@article{hubard2024crossing,
    title={Crossing lemmas for $k$-systems of arcs},
    author={Alfredo Hubard, Hugo Parlier},
    journal={arXiv preprint arXiv:2403.15261},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.15261},
    primaryClass={math.CO cs.CG}
}