Adjacency labelling for proper minor-closed graph classes
Vida Dujmovi\'c, Cyril Gavoille, Gwena\"el Joret, Piotr Micek, Pat Morin, David R. Wood

TL;DR
This paper proves that all proper minor-closed graph classes have adjacency labelling schemes with near-optimal label size, enabling efficient graph representation.
Contribution
It establishes the existence of nearly optimal adjacency labelling schemes for all proper minor-closed graph classes, matching lower bounds up to lower order terms.
Findings
Every proper minor-closed class admits a $(1+o(1)) ext{log}_2 n$-bit adjacency labelling scheme.
For each such class, there exists an $n^{1+o(1)}$-vertex universal graph containing all $n$-vertex graphs in the class as induced subgraphs.
Both results are proven to be optimal up to lower order terms.
Abstract
We show that every proper minor-closed class of graphs admits a -bit adjacency labelling scheme. Equivalently, for every proper minor-closed class and every positive integer there exists an -vertex graph such that every -vertex graph in is isomorphic to an induced subgraph of . Both results are optimal up to the lower order term.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
