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Conference Papers Year : 2020

Adjacency Labelling for Planar Graphs (and Beyond)

Abstract

We show that there exists an adjacency labelling scheme for planar graphs where each vertex of an $n$-vertex planar graph $G$ is assigned a $(1+o(1))\log_2 n$-bit label and the labels of two vertices $u$ and $v$ are sufficient to determine if $uv$ is an edge of $G$. This is optimal up to the lower order term and is the first such asymptotically optimal result. An alternative, but equivalent, interpretation of this result is that, for every $n$, there exists a graph $U_n$ with $n^{1+o(1)}$ vertices such that every $n$-vertex planar graph is an induced subgraph of $U_n$. These results generalize to bounded genus graphs, apex-minor-free graphs, bounded-degree graphs from minor closed families, and $k$-planar graphs.

Dates and versions

hal-02503606 , version 1 (10-03-2020)

Identifiers

Cite

Vida Dujmović, Louis Esperet, Cyril Gavoille, Gwenaël Joret, Piotr Micek, et al.. Adjacency Labelling for Planar Graphs (and Beyond). 61th Annual IEEE Symposium on Foundations of Computer Science, Nov 2020, Virtual conference, United States. ⟨10.1109/FOCS46700.2020.00060⟩. ⟨hal-02503606⟩
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