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A097911 Minimal order of a graph containing as induced subgraphs isomorphic copies of all graphs on n unlabeled nodes. 3
1, 3, 5, 8, 10, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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.

EXAMPLE

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.

CROSSREFS

Cf. A034797, A004401

Sequence in context: A288575 A091309 A027922 * A051611 A258028 A345427

Adjacent sequences:  A097908 A097909 A097910 * A097912 A097913 A097914

KEYWORD

more,nonn

AUTHOR

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

EXTENSIONS

a(5)-a(6) added by James Trimble, Nov 09 2021

STATUS

approved

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Last modified May 22 11:06 EDT 2022. Contains 353949 sequences. (Running on oeis4.)