

A269799


Number of vertices of the fractional matchings polytope for the complete graph on n vertices.


0




OFFSET

1,4


COMMENTS

The fractional matchings polytope of a graph is the set of nonnegative edge weights such that the sum of the weights of the edges incident with any given vertex equals 1.
Sequence up to n=10 computed with PORTA (see links) by Pontus von Brömssen in December 2010.
a(n) equals the number of facets of the polytope P_n defined in Eickmeyer and Yoshida (2008), at least up to n=10.


LINKS

Table of n, a(n) for n=1..10.
Thomas Christof, Sebastian Schenker, PORTA, RuprechtKarlsUniversität Heidelberg.
K. Eickmeyer and R. Yoshida, The Geometry of the NeighborJoining Algorithm for Small Trees, in: Proc. 3rd Int. Conference on Algebraic Biology, 2008, Castle of Hagenberg, Austria, Springer LNCS5147, arXiv:0908.0098 [math.CO], 2009.


EXAMPLE

For n=4 the fractional matchings polytope is the convex hull of the 3 perfect matchings of K_4, so a(4)=3. For n=6, in addition to the 15 perfect matchings of K_6, the 10 pairs of disjoint triangles with edge weights 1/2 are vertices of the polytope, so a(6)=25.


CROSSREFS

Cf. A123023.
Sequence in context: A072398 A134924 A042547 * A079039 A209987 A041103
Adjacent sequences: A269796 A269797 A269798 * A269800 A269801 A269802


KEYWORD

nonn,more


AUTHOR

Pontus von Brömssen, Mar 05 2016


STATUS

approved



