The edge multicoloring problem is that given a graph G and integer demands x(e) for every edge e, assign a set of x(e) colors to edge e, such that adjacent edges have disjoint sets of colors. In the minimum sum edge multicoloring problem the finish time of an edge is defined to be the highest color assigned to it. The goal is to minimize the sum of the finish times. The main result of the paper...

It is a classical result from graph theory that the edges of an l{regular bipartite graph can be colored using exactly l colors so that edges that share an endpoint are assigned diierent colors. In this paper we study two constrained versions of the bipartite edge coloring problem. { Some of the edges adjacent to a pair of opposite vertices of an l-regular bipartite graph are already colored wi...

The problem of edge coloring a bipartite graph is to color the edges so that adjacent edges receive di erent colors An optimal algorithm uses the minimum number of colors to color the edges We consider several approximation algorithms for edge coloring bipartite graphs and show tight bounds on the number of colors they use in the worst case We also present results on the constrained edge colori...

An improved edge-adaptive color interpolation method for Bayer pattern images of single-sensor digital cameras is proposed in this paper. We derive a more accurate color edge classifier by using both intra-channel and interchannel correlation. In order to reduce the aliasing artifacts, missing channel values are interpolated along the edge direction. Experiment results show that the proposed me...

Edge detection has attracted the attention of many researchers and is one of the most important areas in low level computer vision. In recent years, the focus of edge detection has shifted from grayscale single component images to multicomponent color images that utilize the inter-spectral correlation of the neighboring color samples to eliminate color artifacts and increase the accuracy of edg...

We report on a technique for the computation of color edge maps using Hering's Color Space for color coding, and quasiranges, for edge detection. A suitable combination of the resulting edge maps gives an image that is a meaningful visual approximation to the original image. Being an edge map, storage in a small memory space is possible. Finally, a study on the performance depending on the thre...

In this paper, we study a new coloring parameter of graphs called the gap vertexdistinguishing edge coloring. It consists in an edge-coloring of a graph G which induces a vertex distinguishing labeling of G such that the label of each vertex is given by the difference between the highest and the lowest colors of its adjacent edges. The minimum number of colors required for a gap vertex-distingu...

Given a graph G and an edge coloring C of G, a heterochromatic cycle of G is a cycle in which any pair of edges have distinct colors. Let dc(v), named the color degree of a vertex v, be the maximum number of distinct colored edges incident with v. In this paper, some color degree conditions for the existence of heterochromatic cycles are obtained.

The star chromatic index χs(G) of a graph G is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colored. We obtain a near-linear upper bound in terms of the maximum degree ∆ = ∆(G). Our best lower bound on χs in terms of ∆ is 2∆(1 + o(1)) valid for complete graphs. We also consider the special case of cubic graphs, for wh...

A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for th...