Optimal labelling schemes for adjacency, comparability, and reachability

@article{Bonamy2021OptimalLS,
  title={Optimal labelling schemes for adjacency, comparability, and reachability},
  author={Marthe Bonamy and Louis Esperet and Carla Groenland and Alex D. Scott},
  journal={Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing},
  year={2021}
}
  • Marthe Bonamy, Louis Esperet, A. Scott
  • Published 3 December 2020
  • Computer Science, Mathematics
  • Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
We construct asymptotically optimal adjacency labelling schemes for every hereditary class containing 2Ω(n2) n-vertex graphs as n→ ∞. This regime contains many classes of interest, for instance perfect graphs or comparability graphs, for which we obtain an adjacency labelling scheme with labels of n/4+o(n) bits per vertex. This implies the existence of a reachability labelling scheme for digraphs with labels of n/4+o(n) bits per vertex and comparability labelling scheme for posets with labels… 
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AN EXTREMAL PROBLEM IN GRAPH THEORY
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