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Small induced-universal graphs and compact implicit graph representations

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2 Author(s)
Alstrup, S. ; IT Univ., Copenhagen, Denmark ; Rauhe, T.

We show that there exists a graph G with n · 2O(log* n) nodes, where any forest with n nodes is a node-induced subgraph of G. Furthermore, the result implies the existence of a graph with nk2O(log* n) nodes that contains all n-node graphs of fixed arboricity k as node-induced subgraphs. We provide a lower bound of Ω(nk) for the size of such a graph. The upper bound is obtained through a simple labeling scheme for parent queries in rooted trees.

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Foundations of Computer Science, 2002. Proceedings. The 43rd Annual IEEE Symposium on

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