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A059103
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Number of simple, connected, unit-distance graphs on n points realizable in the plane with straight edges all of the same length; lines are permitted to cross.
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5
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OFFSET
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1,3
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COMMENTS
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This counting problem is related to finding the chromatic number of the plane, X(R^2).
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REFERENCES
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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Cf. A350507 (not necessarily connected unit-distance graphs).
Cf. A303792 (connected matchstick graphs).
Cf. A308349 (minimal unit-distance forbidden graphs).
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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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
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STATUS
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approved
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