منابع مشابه
An edge coloring problem for graph products
The edges of the Cartesian product of graphs G x Hare to be colored with the condition that all rectangles, i.e., K2 x K2 subgraphs, must be colored with four distinct colors. The minimum number of colors in such colorings is determined for all pairs of graphs except when G is 5-chromatic and H is 4or 5-chromatic.
متن کاملOn the max-weight edge coloring problem
We study the following generalization of the classical edge coloring problem: Given a weighted graph, find a partition of its edges into matchings (colors), each one of weight equal to the maximum weight of its edges, so that the total weight of the partition is minimized. We explore the frontier between polynomial and NP-hard variants of the problem as well as the approximability of the NP-har...
متن کاملAn Efficient Algorithm for the Nearly Equitable Edge Coloring Problem
An edge coloring of a multigraph is nearly equitable if, among the edges incident to each vertex, the numbers of edges colored with any two colors differ by at most two. It has been proved that the problem of finding a nearly equitable edge coloring can be solved in O(m/k) time, where m and k are the numbers of edges and given colors, respectively. In this paper, we present a recursive algorith...
متن کاملAn Improved Algorithm for the Nearly Equitable Edge-coloring Problem
A nearly equitable edge-coloring of a multigraph is a coloring such that edges incident to each vertex are colored equitably in number. This problem was solved in O(kn2) time, where n and k are the numbers of the edges and the colors, respectively. The running time was improved to be O(n2/k + n|V |) later. We present a more efficient algorithm for this problem that runs in O(n2/k) time. key wor...
متن کاملThe Min-max Edge q-Coloring Problem
In this paper we introduce and study a new problem named min-max edge q-coloring which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer q. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most q different colors, and (b) the maximum size of a colo...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1971
ISSN: 0012-365X
DOI: 10.1016/0012-365x(71)90022-7