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A300531 Matching number of the n-polygon diagonal intersection graph. 3
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)
OFFSET

3,2

COMMENTS

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

LINKS

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

CROSSREFS

Cf. A007569, A291947, A292921, A300550, A300551.

Sequence in context: A243080 A105309 A192572 * A097163 A117186 A155042

Adjacent sequences:  A300528 A300529 A300530 * A300532 A300533 A300534

KEYWORD

nonn,more

AUTHOR

Eric W. Weisstein, Mar 08 2018

EXTENSIONS

a(21)-a(22) from Andrew Howroyd, Mar 12 2018

STATUS

approved

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Last modified March 7 09:46 EST 2021. Contains 341869 sequences. (Running on oeis4.)