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A320727 a(n) is the minimal number of perfect matchings of a graph with 2n vertices that contains exactly three disjoint perfect matchings. 0
3, 4, 5, 6, 6, 8 (list; graph; refs; listen; history; text; internal format)
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 minimal number of PMs that such a graph can have.

LINKS

Table of n, a(n) for n=2..7.

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

Mario Krenn, Xuemei Gu, 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: A198466 A212642 A159624 * A036288 A159077 A049267

Adjacent sequences:  A320724 A320725 A320726 * A320728 A320729 A320730

KEYWORD

nonn,hard,more

AUTHOR

Mario Krenn, Oct 20 2018

STATUS

approved

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Last modified October 14 07:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)