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The Vertex Coloring Algorithm by Ashay Dharwadker (Paperback / softback, 2011)

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About this product

Product Information

We present a new polymial-time algorithm for finding proper m-colorings of the vertices of a graph. We prove that every graph with n vertices and maximum vertex degree Delta must have chromatic number Chi(G) less than or equal to Delta+1 and that the algorithm will always find a proper m-coloring of the vertices of G with m less than or equal to Delta+1. Furthermore, we prove that this condition is the best possible in terms of n and Delta by explicitly constructing graphs for which the chromatic number is exactly Delta+1. In the special case when G is a connected simple graph and is neither an odd cycle r a complete graph, we show that the algorithm will always find a proper m-coloring of the vertices of G with m less than or equal to Delta. In the process, we obtain a new constructive proof of Brooks' famous theorem of 1941. For all kwn examples of graphs, the algorithm finds a proper m-coloring of the vertices of the graph G for m equal to the chromatic number Chi(G). In view of the importance of the P versus NP question, we ask: does there exist a graph G for which this algorithm cant find a proper m-coloring of the vertices of G with m equal to the chromatic number Chi(G)? The algorithm is demonstrated with several examples of famous graphs, including a proper four-coloring of the map of India and two large Mycielski benchmark graphs with hidden minimum vertex colorings. We implement the algorithm in C++ and provide a demonstration program for Microsoft Windows.

Product Identifiers

Publisher
Createspace Independent Publishing Platform
ISBN-10
1466391324
ISBN-13
9781466391321
eBay Product ID (ePID)
189523846

Product Key Features

Author
Ashay Dharwadker
Format
Paperback / Softback, Trade Paperback (US) ,Unsewn / Adhesive Bound
Language
English
Topic
Computing: Professional & Programming

Additional Product Features

Content Note
Colour Illustrations
Date of Publication
02/10/2011
Country of Publication
United States

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