منابع مشابه
On k-partitioning of Hamming Graphs
We consider the graphs Hn a defined as the Cartesian products of n complete graphs with a vertices each. Let an edge cut partition the vertex set of a graph into k subsets A1, . . . , Ak with ||Ai| − |Aj || ≤ 1. We consider the problem of determining the minimal size of such a cut for the graphs defined above and present bounds and asymptotic results for some specific values of k.
متن کاملDISTANCE k COLORINGS OF HAMMING GRAPHS
A coloring of the vertices of a graph G is a distance k coloring of G if and only if any two vertices lying on a path of length less than or equal to k are given different colors. Hamming graphs are Cartesian (or box) products of complete graphs. In this paper, we will consider the interaction between coding theory and distance k colorings of Hamming graphs.
متن کاملComplete k-ary trees and Hamming graphs
A Hamming graph H(b, n) of base b and dimension n has vertex set {X = x1x2 . . . xn : xi ∈ {0, 1, . . . , b − 1}, for 1 ≤ i ≤ n} and edge set {(X, Y ) : X and Y differ in exactly one bit position}. In this paper, we are concerned with the following problem: Given positive integers b, k and h, what is the minimum integer m = m(b, k, h) such that the complete k-ary tree, T k h , of height h, is a...
متن کاملOn Bounds for the k-Partitioning of Graphs
Let an edge cut partition the vertex set of a graph into k disjoint subsets A1, . . . , Ak with ||Ai| − |Aj || ≤ 1. We consider the problem of determining the minimal size of such a cut for a given graph. For this we introduce a new lower bound method which is based on the solution of an extremal set problem and present bounds for some graph classes based on Hamming graphs.
متن کاملPartitioning Generic Graphs into K Balanced Subgraphs
Graph partitioning is a classical graph theory problem that has proven to be NP-hard. Most of the research in literature has focused its attention on a particular case of the problem called the graph bisection problem, where k = 2, such that the parts have approximately equal weight and minimizing the size of the edge cut. In this article, we describe how to obtain balanced partitioning on a gi...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1999
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00070-0