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 (Dujmović 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).
From: Pat Morin [view email]
[v1]
Thu, 7 May 2026 17:32:24 UTC (150 KB)
[v2]
Fri, 8 May 2026 11:59:12 UTC (150 KB)
[v3]
Mon, 13 Jul 2026 17:39:35 UTC (50 KB)
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