A Better than "Best Possible" Algorithm to Edge Color Multigraphs

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.

Approximating 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...

Improving a Family of Approximation Algorithms to Edge Color Multigraphs

Edge-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...

On Interval Non-Edge-Colorable Eulerian Multigraphs

An edge-coloring of a multigraph G with colors 1, . . . , t is called an interval t-coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In this note, we show that all Eulerian multigraphs with an odd number of edges have no interval coloring. We also give some methods for constructing of interval non-edge-colorable ...