منابع مشابه
The Polytope of Degree Partitions
The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. Let DP(n) (respectively, DS(n)) denote the convex hull of all degree partitions (respectively, degree sequences) of simple graphs on the vertex set [n] = {1, 2, . . . , n}. We think of DS(n) as the symmetrization of DP(n) and DP(n) as the asymmetric part of DS(n). The polytope DS(n) is a well st...
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We determine the extreme points and facets of the convex hull of all dual degree partitions of simple graphs on n vertices. 1
متن کاملThe square root rank of the correlation polytope is exponential
The square root rank of a nonnegative matrix A is the minimum rank of a matrix B such that A = B ◦B, where ◦ denotes entrywise product. We show that the square root rank of the slack matrix of the correlation polytope is exponential. Our main technique is a way to lower bound the rank of certain matrices under arbitrary sign changes of the entries using properties of the roots of polynomials in...
متن کاملPartitions of a Polytope and Mappings of a Point Set to Facets
Three theorems of this paper generalize previous results of the author on conjectures of A. Bezdek and V. V. Proizvolov. They show the existence of mappings from a given point set to the set of facets of a given polytope that satistfy some special conditions. Developing the same technique, some results on convex polytope partitions are presented, two of them dealing with partitions with prescri...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2014
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-014-0526-5