

A300531


Matching number of the npolygon 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



