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

1, 2, 5, 9, 21, 28, 67, 85, 170, 156, 364, 385, 690, 696, 1198, 927, 1947, 1930, 3003, 2981

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