Record Details

The polytope of degree partitions

DSpace at IIT Bombay

View Archive Info
 
 
Field Value
 
Title The polytope of degree partitions
 
Creator BHATTACHARYA, A
SIVASUBRAMANIAN, S
SRINIVASAN, MK
 
Subject degree sequences
graphs
 
Description 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 degree partitions (respectively, degree sequences) of all simple graphs on the vertex set [n]. The polytope of degree sequences has been very well studied. In this paper we study the polytope of degree partitions. We show that adding the inequalities x(1) >= x(2) >= ... >= x(n) to a linear inequality description of the degree sequence polytope yields a linear inequality description of the degree partition polytope and we show that the extreme points of the degree partition polytope are the 2(n-1) threshold partitions (these are precisely those extreme points of the degree sequence polytope that have weakly decreasing coordinates). We also show that the degree partition polytope has 2(n-2) (2n - 3) edges and (n(2)-3n + 12)/2 facets, for n >= 4. Our main tool is an averaging transformation on real sequences defined by repeatedly averaging over the ascending runs.
 
Publisher ELECTRONIC JOURNAL OF COMBINATORICS
 
Date 2011-07-21T15:21:50Z
2011-12-26T12:52:03Z
2011-12-27T05:39:00Z
2011-07-21T15:21:50Z
2011-12-26T12:52:03Z
2011-12-27T05:39:00Z
2006
 
Type Article
 
Identifier ELECTRONIC JOURNAL OF COMBINATORICS, 13(1), -
1077-8926
http://dspace.library.iitb.ac.in/xmlui/handle/10054/5906
http://hdl.handle.net/10054/5906
 
Language en