Edge-colourings of Graphs
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A Class of Graphs of f-Class 1. Soft Edge Coloring.
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Journal of Applied Mathematics and Computing 22 , Electronic Notes in Discrete Mathematics 25 , Discrete Applied Mathematics :8, Theoretical Computer Science :3, Journal of Scheduling 9 :1, Applied Mathematics Letters 19 :1, IEE Proceedings - Communications :3, Approximation Algorithms for Path Coloring in Trees.
Efficient Approximation and Online Algorithms, Journal of Interconnection Networks 06 , Mathematics of Operations Research 30 :4, Electronic Notes in Discrete Mathematics 22 , Journal of Graph Theory 49 :4, Journal of Computational Biology 12 :5, Journal of Computer and System Sciences 70 :3, Journal of Algorithms 55 :1, Journal of Combinatorial Optimization 9 :1, Advances in Informatics, Experimental and Efficient Algorithms, Electronic Notes in Discrete Mathematics 18 , Discrete Applied Mathematics :1, Electronic Notes in Discrete Mathematics 17 , International Journal of Foundations of Computer Science 15 , Back Matter.
Algorithmische Graphentheorie, More on a Binary-Encoded Coloring Formulation. Multicoloring: Problems and Techniques. Information Processing Letters 88 :4, Journal of Parallel and Distributed Computing 63 :9, Journal of Graph Theory 43 :2, Discrete Applied Mathematics :3, Euromicro Symposium on Digital System Design, On the coloration of perfect graphs. Recent Advances in Algorithms and Combinatorics, On Generalized Gossiping and Broadcasting.
Algorithms - ESA , Journal of Algorithms 45 :2, Networks 40 :1, European Journal of Combinatorics 23 :3, Information Processing Letters 81 :4, Coloring Algorithms on Subcubic Graphs. Algorithms — ESA , Discrete Geometry for Computer Imagery, Approximating Maximum Edge Coloring in Multigraphs. Approximation Algorithms for Combinatorial Optimization, On the b-Chromatic Number of Graphs. Wavelength Assignment. Multiwavelength Optical Networks, Journal of Algorithms 41 :1, Automata, Languages and Programming, Complexity of Partial Covers of Graphs.
Journal of Algorithms 37 :2, Luca Trevisan. Generalized H-Coloring of Graphs. How Helpers Hasten h-Relations. Encyclopaedia of Mathematics, Edge Colouring Reduced Indifference Graphs. Journal of Graph Theory 32 :4, Information Sciences , Journal of Combinatorial Theory, Series B 75 :2, Operations Research Letters 24 , Journal of Combinatorial Theory, Series B 74 :2, Information Processing Letters 68 :1, Theoretical Computer Science :2, Discrete Applied Mathematics 85 :1, Discrete Applied Mathematics 82 , Alexander Schrijver.
Models for Optically Interconnected Networks.
Further reading
Probabilistic Analysis of Algorithms. Probabilistic Methods for Algorithmic Discrete Mathematics, Advances in Engineering Software 28 :9, Discrete Applied Mathematics 79 , Journal of Combinatorial Theory, Series B 71 :1, Theoretical Computer Science :1, Carsten Thomassen. Discrete Applied Mathematics 76 , Information Processing Letters 62 :6, Applied Mathematics and Computation 83 :1, Complexity of colored graph covers I.
Colored directed multigraphs. A parallel approximation algorithm for resource constrained scheduling and bin packing. Solving Irregularly Structured Problems in Parallel, Approximation on the web: A compendium of NP optimization problems.
Edge coloring
Randomization and Approximation Techniques in Computer Science, Operations Research and Discrete Analysis, Parallel Algorithms and Complexity. Parallel Computing in Optimization, European Journal of Operational Research 94 :2, Combinatorics, Probability and Computing 5 :1, Efficient wavelength routing on directed fiber trees. Algorithms — ESA '96, Mathematical Systems Theory 28 :6, Information Processing Letters 55 :6, Information Processing Letters 54 :5, International Journal of Wireless Information Networks 2 :2, Chapter 3 Matching.
Network Models, Structure in approximation classes. Journal of Graph Theory 19 :1, Complexity of graph covering problems.
In the case of bipartite graphs or an optimal edge coloring of these graphs can be found. An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors.
On edge-colouring indifference graphs. Near-optimal distributed edge coloring. Algorithms — ESA '95, Algorithms for finding f-colorings of partial k-trees. Algorithms and Computations, Edge-coloring algorithms. Computer Science Today, Simple reduction of f-colorings to edge-colorings. Journal of Computer and System Sciences 49 :3, Discrete Applied Mathematics 51 , Computational Complexity 4 :2, Some results concerning the complexity of interval edge-colorings of graphs.
Tight approximations for resource constrained scheduling problems. Algorithms — ESA '94, A parallel algorithm for edge-coloring partial k-trees. Edge-coloring and f-coloring for various classes of graphs. Operations Research Letters 13 :4, Networks 23 :2, A linear algorithm for edge-coloring partial k-trees. Algorithms—ESA '93, Journal of Graph Theory 16 :2, Discrete Applied Mathematics 36 :1, Operations Research Letters 10 :6, Information and Computation 91 :1, Discrete Applied Mathematics 30 :1, Scheduling file transfers under port and channel constraints.
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ISA'91 Algorithms, Journal of Algorithms 11 :4, Combinatorica 10 :4, Journal of Graph Theory 14 :5, Bill Jackson. Discrete Applied Mathematics 27 :3, Discrete Mathematics 82 :2, Journal of Graph Theory 14 :2, Theoretical Computer Science 71 :3, Journal of Algorithms 11 :1, Journal of Combinatorial Theory, Series B 48 :1, Journal of Algorithms 10 :1, Discrete Mathematics 74 , Graph Colouring and Variations, Hints help you try the next step on your own.
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Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. MathWorld Book. Terms of Use. Contact the MathWorld Team. For example, the following can be colored minimum 3 colors.
Vertex coloring is the starting point of the subject, and other coloring problems can be transformed into a vertex version. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems are often stated and studied as is. That is partly for perspective, and partly because some problems are best studied in non-vertex form, as for instance is edge coloring. The convention of using colors originates from coloring the countries of a map, where each face is literally colored.
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This was generalized to coloring the faces of a graph embedded in the plane. By planar duality it became coloring the vertices, and in this form it generalizes to all graphs. In mathematical and computer representations, it is typical to use the first few positive or non negative integers as the "colors". In general, one can use any finite set as the "color set". The nature of the coloring problem depends on the number of colors but not on what they are.
Consider the currently picked vertex Colour it with the lowest numbered colour that has not been used on any previously colored vertices adjacent to it.