• Corpus ID: 237371963

Induced universal graphs for families of small graphs

@article{Trimble2021InducedUG,
  title={Induced universal graphs for families of small graphs},
  author={James Trimble},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.00075}
}
We present exact and heuristic algorithms that find, for a given family of graphs, a graph that contains each member of the family as an induced subgraph. For 0 ≤ k ≤ 6, we give the minimum number of vertices f(k) in a graph containing all k-vertex graphs as induced subgraphs, and show that 16 ≤ f(7) ≤ 18. For 0 ≤ k ≤ 5, we also give the counts of such graphs, as generated by brute-force computer search. We give additional results for small graphs containing all trees on k vertices. 

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