%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