Adjacency labeling schemes and induced-universal graphs

Stephen Alstrup, Haim Kaplan, Mikkel Thorup, Uri Zwick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We describe a way of assigning labels to the vertices of any undirected graph on up to n vertices, each composed of n/2+ O(1) bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an n/2+O(log n) bound of Moon. As a consequence, we obtain an induced-universal graph for n-vertex graphs containing only O(2n/2) vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs.

Original languageEnglish
Title of host publicationSTOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Electronic)9781450335362
StatePublished - 14 Jun 2015
Event47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States
Duration: 14 Jun 201517 Jun 2015

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference47th Annual ACM Symposium on Theory of Computing, STOC 2015
Country/TerritoryUnited States


  • Adjacency labeling schemes
  • Induced-universal graphs


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