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
Noga 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.
James Trimble, Induced universal graphs for families of small graphs, arXiv:2109.00075 [math.CO], 2021.
James Trimble, Partitioning algorithms for induced subgraph problems, Ph.D. Thesis, Univ. of Glasgow (Scotland, 2023), 134.
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
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