## Small Induced-Universal Graphs and Compact Implicit Graph Representations (2002)

by
Stephen Alstrup
,
Theis Rauhe

Venue: | In Proc. 43’rd annual IEEE Symp. on Foundations of Computer Science |

Citations: | 12 - 0 self |

### BibTeX

@INPROCEEDINGS{Alstrup02smallinduced-universal,

author = {Stephen Alstrup and Theis Rauhe},

title = {Small Induced-Universal Graphs and Compact Implicit Graph Representations},

booktitle = {In Proc. 43’rd annual IEEE Symp. on Foundations of Computer Science},

year = {2002},

pages = {53--62}

}

### OpenURL

### Abstract

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