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arXiv · 2310.07893

Borel line graphs

James Anderson·Anton Bernshteyn
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Abstract

We characterize Borel line graphs in terms of 10 forbidden induced subgraphs, namely the 9 finite graphs from the classical result of Beineke together with a 10th infinite graph associated to the equivalence relation $\mathbb{E}_0$ on the Cantor space. As a corollary, we prove a partial converse to the Feldman--Moore theorem, which allows us to characterize all locally countable Borel line graphs in terms of their Borel chromatic numbers.

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James Anderson, Anton Bernshteyn. 2023-10-11. Borel line graphs. https://doi.org/10.1017/jsl.2024.50

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