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...
متن کاملThe 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 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 کاملMonochromatic bounded degree subgraph partitions
Let F = {F1, F2, . . .} be a sequence of graphs such that Fn is a graph on n vertices with maximum degree at most ∆. We show that there exists an absolute constant C such that the vertices of any 2-edge-colored complete graph can be partitioned into at most 2C∆log ∆ vertex disjoint monochromatic copies of graphs from F . If each Fn is bipartite, then we can improve this bound to 2C∆; this resul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1072