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Minimal order of a graph containing as induced subgraphs isomorphic copies of all graphs on n unlabeled nodes.
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%I #19 Jan 20 2023 18:05:07

%S 1,3,5,8,10,14

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

%C A graph that contains as induced subgraphs isomorphic copies of all graphs in a family F is called induced universal for F. - _James Trimble_, Nov 09 2021

%C 16 <= a(7) <= 18 (Trimble, 2021). - _James Trimble_, Nov 09 2021

%H Noga Alon, <a href="https://doi.org/10.1007/s00039-017-0396-9">Asymptotically optimal induced universal graphs</a>, Geometric and Functional Analysis, 27(1):1-32, 2017.

%H Richard Rado, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa9/aa9133.pdf">Universal graphs and universal functions</a>, Acta Arith. 9 (1964), 331-340.

%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.

%e a(3) = 5 as (P1 + K1)*K1 + K1 has 5 vertices and is easily seen minimal for 3. Here P1 is the path with one edge and K1 is an isolated vertex.

%Y Cf. A034797, A004401

%K more,nonn

%O 1,2

%A Dan Schwarz (dan_schwarz(AT)hotmail.com), Sep 04 2004

%E a(5)-a(6) added by _James Trimble_, Nov 09 2021