# 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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