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Minimal order of a graph containing as induced subgraphs isomorphic copies of all trees on n unlabeled nodes.
2

%I #42 Jan 20 2023 18:05:33

%S 1,2,3,5,7,9,11,13

%N Minimal order of a graph containing as induced subgraphs isomorphic copies of all trees on n unlabeled nodes.

%C a(n) is the minimal order of an induced universal graph for the family of trees on n vertices.

%C a(9) <= 15 and a(10) <= 18 (Trimble, 2021).

%H James Trimble, <a href="https://arxiv.org/abs/2109.00075">Induced universal graphs for families of small graphs</a>, arXiv:2109.00075 [math.CO], 2021.

%H James Trimble, <a href="http://dx.doi.org/10.5525/gla.thesis.83350">Partitioning algorithms for induced subgraph problems</a>, Ph.D. Thesis, Univ. of Glasgow (Scotland, 2023), 134.

%Y Cf. A004401, A097911.

%K nonn,more

%O 1,2

%A _James Trimble_, Nov 09 2021