Optimal induced universal graphs and adjacency labeling for trees

Research output: Contribution to journalJournal articleResearchpeer-review

In this article, we show that there exists a graph G with O(n) nodes such that any forest of n nodes is an induced subgraph of G Furthermore, for constant arboricity k, the result implies the existence of a graph with O(nk) nodes that contains all n-node graphs of arboricity k as node-induced subgraphs, matching a Ω(nk) lower bound of Alstrup and Rauhe. Our upper bounds are obtained through a log2 n + O(1) labeling scheme for adjacency queries in forests. We hereby solve an open problem being raised repeatedly over decades by authors such as Kannan et al., Chung, and Fraigniaud and Korman.

Original languageEnglish
Article number27
JournalJournal of the ACM
Volume64
Issue number4
Number of pages22
ISSN0004-5411
DOIs
Publication statusPublished - Sep 2017

    Research areas

  • Adjacency labeling, Graph theory, Induced universal graphs, Trees, XML

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