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A097911
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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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3
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OFFSET
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1,2
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COMMENTS
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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
16 <= a(7) <= 18 (Trimble, 2021). - James Trimble, Nov 09 2021
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LINKS
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Table of n, a(n) for n=1..6.
N. Alon, Asymptotically optimal induced universal graphs, Geometric and Functional Analysis, 27(1):1-32, 2017.
Richard Rado, Universal graphs and universal functions, Acta Arith. 9 (1964), 331-340.
J. Trimble, Induced universal graphs for families of small graphs, arXiv:2109.00075 [math.CO], 2021.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A034797, A004401
Sequence in context: A288575 A091309 A027922 * A051611 A258028 A345427
Adjacent sequences: A097908 A097909 A097910 * A097912 A097913 A097914
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KEYWORD
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more,nonn
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AUTHOR
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Dan Schwarz (dan_schwarz(AT)hotmail.com), Sep 04 2004
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EXTENSIONS
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a(5)-a(6) added by James Trimble, Nov 09 2021
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STATUS
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approved
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