OFFSET
1,3
COMMENTS
This counting problem is related to finding the chromatic number of the plane, X(R^2).
REFERENCES
K. B. Chilakamarri and C. R. Mahoney, Maximal and minimal forbidden unit-distance graphs in the plane, Bulletin of the ICA, 13 (1995), 35-43.
LINKS
Aidan Globus and Hans Parshall, Small unit-distance graphs in the plane, arXiv:1905.07829 [math.CO], 2019.
Matthew McAndrews, Simple Connected Units Distance Graphs Through 6 Vertices
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Unit-Distance Graph
EXAMPLE
a(4)=5 because the complete graph on 4 points cannot be realized in the plane with all edges of equal length. All the other connected graphs with 4 points can be realized.
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
David S. Newman, Feb 13 2001
EXTENSIONS
a(6) has been updated to reflect the fact that it has recently been proved to be 51 rather than 50. - Matthew McAndrews, Feb 21 2016
a(7) from Hans Parshall, May 03 2018
a(8)-a(9) from Hans Parshall, May 21 2019
STATUS
approved