منابع مشابه
The Polytope of Dual Degree Partitions
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 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...
متن کاملThe Excess Degree of a Polytope
We define the excess degree ξ(P ) of a d-polytope P as 2f1− df0, where f0 and f1 denote the number of vertices and edges, respectively. We first prove that the excess degree of a d-polytope does not take every natural number: the smallest possible values are 0 and d − 2, and the value d − 1 only occurs when d = 3 or 5. On the other hand, for fixed d , the number of values not taken by the exces...
متن کاملDegree-bounded vertex partitions
This paper studies degree-bounded vertex partitions, considers analogues for wellknown results on the chromatic number and graph perfection, and presents two algorithms for constructing degree-bounded vertex partitions. The first algorithm minimizes the number of partition classes. The second algorithm minimizes a weighted sum of the partition classes where the weight of a partition class depen...
متن کاملA dual polytope from the SYZ construction
For a particular toric variety, I explore to what extent the SYZ conjecture applied to the orbits of the torus action gives the mirror manifold, in the sense of Batyrev’s mirror construction using reflexive polytopes.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.05.022