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A300531
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Matching number of the n-polygon diagonal intersection graph.
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3
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1, 2, 5, 9, 21, 28, 67, 85, 170, 156, 364, 385, 690, 696, 1198, 927, 1947, 1930, 3003, 2981
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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3,2
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COMMENTS
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Conjecturally, a matching exists for every n with at most one unmatched vertex. This would imply a(n) = floor(A007569(n)/2). A computer search, using a simple nonbacktracking algorithm, has shown the existence of such matchings up to n = 22 and indeed for small n there are large numbers of maximum matchings (A292921). Such a matching could also be constructed from a Hamiltonian path (A300551) by selecting every other edge, so a proof that these graphs are Hamiltonian would also suffice. - Andrew Howroyd, Mar 12 2018
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LINKS
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Table of n, a(n) for n=3..22.
Eric Weisstein's World of Mathematics, Matching Number
Eric Weisstein's World of Mathematics, Polygon Diagonal Intersection Graph
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CROSSREFS
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Cf. A007569, A291947, A292921, A300550, A300551.
Sequence in context: A243080 A105309 A192572 * A097163 A117186 A155042
Adjacent sequences: A300528 A300529 A300530 * A300532 A300533 A300534
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KEYWORD
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nonn,more
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AUTHOR
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Eric W. Weisstein, Mar 08 2018
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EXTENSIONS
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a(21)-a(22) from Andrew Howroyd, Mar 12 2018
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STATUS
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approved
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