منابع مشابه
Edge-coloring series-parallel multigraphs
We give a simpler proof of Seymour’s Theorem on edge-coloring series-parallel multigraphs and derive a linear-time algorithm to check whether a given series-parallel multigraph can be colored with a given number of colors.
متن کاملEdge coloring multigraphs without small dense subsets
One consequence of an old conjecture of Goldberg and Seymour about the chromatic index of multigraphs would be the following statement. Suppose G is a multigraph with maximum degree ∆, such that no vertex subset S of odd size at most ∆ induces more than (∆+1)(|S|−1)/2 edges. Then G has an edge coloring with ∆ + 1 colors. Here we prove a weakened version of this statement.
متن کاملApproximating Maximum Edge Coloring in Multigraphs
We study the complexity of the following problem that we call Max edge t-coloring : given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G that has chromatic index at most t). We show that for every fixed t ≥ 2 there is some > 0 such that i...
متن کاملEdge-Coloring Bipartite Multigraphs to Select Network Paths
We consider the idea of using a centralized controller to schedule network traffic within a datacenter and implement an algorithm that edge-colors bipartite multigraphs to select the paths that packets should take through the network. We implement three different data structures to represent the bipartite graphs: a matrix data structure, an adjacency list data structure, and an adjacency list d...
متن کاملAn NC Parallel Algorithm for Edge-Coloring Series-Parallel Multigraphs
Many combinatorial problems can be efficiently solved in parallel for series]parallel multigraphs. The edge-coloring problem is one of a few combinatorial problems for which no NC parallel algorithm has been obtained for series]parallel multigraphs. This paper gives an NC parallel algorithm for the Ž . Ž . problem on series]parallel multigraphs G. It takes O log n time with O Dnrlog n processor...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.04.017