Chromatic polynomials and chromaticity of some linear h-hypergraphs - Softcover

Kashif, Muhammad

Softcover

ISBN 10: 3639348230 ISBN 13: 9783639348231

Verlag: VDM Verlag Dr. Müller, 2011

Inhaltsangabe

For a century, one of the most famous problems in mathematics was to prove the four-color theorem.In 1912, George Birkhoff proposed a way to tackling the four-color conjecture by introduce a function P(M, t), defined for all positive integer t, to be the number of proper t-colorings of a map M. This function P(M, t)in fact a polynomial in t is called chromatic polynomial of M. If one could prove that P(M, 4)>0 for all maps M, then this would give a positive answer to the four-color problem. In this book, we have proved the following results: (1)Recursive form of the chromatic polynomials of hypertree, Centipede hypergraph, elementary cycle, Sunlet hypergraph, Pan hypergraph, Duth Windmill hypergraph, Multibridge hypergraph, Generalized Hyper-Fan, Hyper-Fan, Generalized Hyper-Ladder and Hyper-Ladder and also prove that these hypergraphs are not chromatically uniquein the class of sperenian hypergraphs. (2)Tree form and Null graph representation of the chromatic polynomials of elementary cycle, uni-cyclic hypergraph and sunflower hypergrpah. (3)Generalization of a result proved by Read for graphs to hypergraphs and prove that these kinds of hypergraphs are not chromatically unique.

Details zur Ausgabe

• Verlag: VDM Verlag Dr. Müller
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 3639348230
• ISBN 13: 9783639348231
• Einband: Taschenbuch
• Anzahl der Seiten: 120
• Kontakt zum Hersteller: Noor Publishing; customerservice@vdm-vsg.de; ; Brivibas gatve 197; Riga; 1039; Lettland