On dual-ABAB-free and related hypergraphs
<|reference_start|>On dual-ABAB-free and related hypergraphs: Geometric motivations warranted the study of hypergraphs on ordered vertices that have no pair of hyperedges that induce an alternation of some given length. Such hypergraphs are called ABA-free, ABAB-free and so on. Since then various coloring and other combinatorial results were proved about these families of hypergraphs. We prove a characterization in terms of their incidence matrices which avoids using the ordering of the vertices. Using this characterization, we prove new results about the dual hypergraphs of ABAB-free hypergraphs. In particular, we show that dual-ABAB-free hypergraphs are not always proper $2$-colorable even if we restrict ourselves to hyperedges that are larger than some parameter $m$.<|reference_end|>
@article{keszegh2024on,
    title={On dual-ABAB-free and related hypergraphs},
    author={Bal'azs Keszegh, D"om"ot"or P'alv"olgyi},
    journal={arXiv preprint arXiv:2406.13321},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.13321},
    primaryClass={math.CO cs.CG}
}