The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)



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.


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).


Cf. A003436.

Sequence in context: A198466 A212642 A159624 * A036288 A159077 A049267

Adjacent sequences:  A320724 A320725 A320726 * A320728 A320729 A320730




Mario Krenn, Oct 20 2018



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)