The polytope of degree partitions

Details The polytope of degree partitions The polytope of degree partitions

2005-12-16

arxiv.org/abs/math/0512402v1

Mathematics

Combinatorics

21 pages

Scientific paper

The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of all degree partitions (respectively, degree sequences) of a fixed length. We think of the degree sequence polytope as the symmetrization of the degree partition polytope and the degree partition polytope as the asymmetric part of the degree sequence polytope. The degree sequence polytope is a well studied object with formulas (generating functions) known for its face numbers, volume, and number of lattice points. We study the degree partition polytope and determine its extreme points, edges, and facets. In particular, the degree partition polytope on n vertices has 2^{n-1} extreme points.

Affiliated with

Also associated with

No associations

Rating

The polytope of degree partitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The polytope of degree partitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The polytope of degree partitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-112405