A301560 Matching number of the n-odd graph.

0, 1, 5, 17, 63, 231, 858, 3217, 12155, 46189, 176358, 676039, 2600150, 10029150, 38779380, 150270097, 583401555, 2268783825, 8836315950, 34461632205, 134564468610, 526024740930, 2058357681900, 8061900920775, 31602651609438, 123979633237026, 486734856412028

Offset

1,3

Comments

The n-odd graph is known to be Hamiltonian for 4 <= n <= 14. Hamiltonian graphs always have a matching with at most one unmatched vertex. - Andrew Howroyd, Mar 23 2018 [Now known for all n >= 4. - Pontus von Brömssen, May 01 2020]

Links

Table of n, a(n) for n=1..27.

T. Mütze, J. Nummenpalo, B. Walczak, Sparse Kneser graphs are Hamiltonian, arXiv:1711.01636, [math.CO], 2017.

Eric Weisstein's World of Mathematics, Independent Edge Set

Eric Weisstein's World of Mathematics, Matching Number

Eric Weisstein's World of Mathematics, Odd Graph

Wikipedia, Odd Graph

Formula

a(n) = floor(binomial(2*n - 1, n - 1)/2).

Crossrefs

Cf. A301557.

Sequence in context: A146444 A128073 A051736 * A099528 A149667 A149668

Adjacent sequences: A301557 A301558 A301559 * A301561 A301562 A301563

Keyword

nonn

Author

Eric W. Weisstein, Mar 23 2018

Extensions

a(8)-a(14) from Andrew Howroyd, Mar 23 2018

More terms from Pontus von Brömssen, May 01 2020

Status

approved