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arXiv · 2605.06616

Adjacency labelling for proper minor-closed graph classes

Vida Dujmović·Cyril Gavoille·Gwenaël Joret·Piotr Micek·Pat Morin·David R. Wood
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Abstract

We show that every proper minor-closed class of graphs admits a $(1+o(1))\log_2 n$-bit adjacency labelling scheme. Equivalently, for every proper minor-closed class $\mathcal{G}$ and every positive integer $n$ there exists an $n^{1+o(1)}$-vertex graph $U$ such that every $n$-vertex graph in $\mathcal{G}$ is isomorphic to an induced subgraph of $U$. Both results are optimal up to the lower order term. They generalize the corresponding results for planar graphs and apex-minor-free classes (Dujmovi\'c et al., J.~ACM 2021) to all proper minor-closed classes, answering the open question raised in that paper and anticipated earlier by Bonamy, Gavoille, and Pilipczuk (SODA 2020).

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Vida Dujmović, Cyril Gavoille, Gwenaël Joret, Piotr Micek, Pat Morin, David R. Wood. 2026-05-07. Adjacency labelling for proper minor-closed graph classes. https://arxiv.org/abs/2605.06616

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