A316531 a(n) is the maximum number of perfect matchings of a graph with 2n vertices that contains exactly three disjoint perfect matchings.

3, 6, 9, 13, 20, 32, 52

Offset

2,1

Comments

Take a cycle graph which has two perfect matchings (PM), and add one PM that is disjoint to it. The number of possible PMs one can add is given by A003436. One ends up with a set of three disjoint perfect matchings (where disjoint means that each edge is an element of maximally one PM), but the graph will have more PMs. This sequence describes the maximum number of PMs that such a graph can have.

Links

Table of n, a(n) for n=2..8.

Ilya Bogdanov, Graphs with only disjoint perfect matchings, MathOverflow.

Mario Krenn, Xuemei Gu, and Anton Zeilinger, Quantum experiments and graphs: Multiparty states as coherent superpositions of perfect matchings, Physical review letters, 119(24), 240403 (2017).

Crossrefs

Cf. A003436.

Sequence in context: A137041 A153006 A181970 * A242339 A086838 A161669

Adjacent sequences: A316528 A316529 A316530 * A316532 A316533 A316534

Keyword

nonn,hard,more

Author

Mario Krenn, Oct 20 2018

Extensions

a(8) from Mario Krenn, Jul 20 2024

Status

approved