Affiliation:
1. Laboratoire G‐SCOP CNRS, Univ. Grenoble Alpes Grenoble France
2. Département d'Informatique Université libre de Bruxelles Brussels Belgium
3. School of Computer Science Carleton University Ottawa Canada
Abstract
AbstractWe show that for every integer , there exists a graph with vertices and edges such that every ‐vertex planar graph is isomorphic to a subgraph of . The best previous bound on the number of edges was , proved by Babai, Chung, Erdős, Graham, and Spencer in 1982. We then show that for every integer , there is a graph with vertices and edges that contains induced copies of every ‐vertex planar graph. This significantly reduces the number of edges in a recent construction of the authors with Dujmović, Gavoille, and Micek.
Cited by
2 articles.
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1. Product structure of graph classes with bounded treewidth;Combinatorics, Probability and Computing;2023-12-07
2. Proof of the Clustered Hadwiger Conjecture;2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS);2023-11-06