Optimal induced universal graphs and adjacency labeling for trees

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

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.

OriginalsprogEngelsk
Artikelnummer27
TidsskriftJournal of the ACM
Vol/bind64
Udgave nummer4
Antal sider22
ISSN0004-5411
DOI
StatusUdgivet - sep. 2017

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