Download or read book Chromaticity of Hypergraphs written by Syed Ahtsham Ul Haq Bokhary and published by LAP Lambert Academic Publishing. This book was released on 2011-10 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: The coloring the vertices of a graph is one of the fundamental concepts of graph theory. It is widely believed that coloring was first mentioned in 1852 when Francis Guthrie asked if four colors are enough to color any geographic map in such a way that no two countries sharing a common border would have the same color. If we denote the countries by points in the plane and connect each pair of points that correspond to two countries with a common border by a curve, we obtain a planar graph. The celebrated four color problem asks if every planer graph can be colored with 4 colors. The four color problem became one of the most famous problem in discrete mathematics of the 20th century. This has spawned the development of many useful tools for solving graph coloring problems. The coloring of hypergraphs started in 1966 when P. Erdos and A. Hajnal introduced the notion of coloring of a hypergraph and obtained the first important results. Since then many results in graph colorings have been extended to hyper- graphs. This work focuses on the chromatic polynomial and chromatic uniqueness of hypergraphs.
Download or read book Coloring Mixed Hypergraphs Theory Algorithms and Applications written by Vitaly Ivanovich Voloshin and published by American Mathematical Soc.. This book was released on 2002 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications. Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory ofcolorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and the maximum number of colors. This feature pervades the theory, methods, algorithms, and applications of mixed hypergraph coloring. The book has broad appeal. It will be of interest to bothpure and applied mathematicians, particularly those in the areas of discrete mathematics, combinatorial optimization, operations research, computer science, software engineering, molecular biology, and related businesses and industries. It also makes a nice supplementary text for courses in graph theory and discrete mathematics. This is especially useful for students in combinatorics and optimization. Since the area is new, students will have the chance at this stage to obtain results that maybecome classic in the future.
Download or read book Color critical Hypergraphs written by Donovan Ross Hare and published by . This book was released on 1987 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics in the 21st Century written by Pierre Cartier and published by Springer. This book was released on 2014-11-15 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology. Several papers on computational and applied mathematics such as wavelet analysis, quantum mechanics, piecewise linear modeling, cosmological models of super symmetry, fluid dynamics, interpolation theory, optimization, ergodic theory and games theory are also presented.
Download or read book The Circular Chromatic Number of Hypergraphs written by Laura Margret Diane Shepherd and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalization of the circular chromatic number to hypergraphs is devel-oped. Circular colourings of graphs and hypergraphs are first discussed and it is shown that the circular chromatic number of a graph is the same regard-less of whether the hypergraph or graph definition is used. After presenting a few basic results, some examples of circular chromatic numbers of various families of hypergraphs are given. Subsequently, the concepts of the star chromatic number and the arc chromatic number are introduced. Specif?ically, both numbers are shown to be equivalent to the circular chromatic number. Finally the relationship between the imbalance of a hypergraph and the circular chromatic number is explored and a classical result of Minty is deduced.
Download or read book The Circular Chromatic Number of Hypergraphs written by Laura Margret Diane Shepherd and published by . This book was released on 2005 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalization of the circular chromatic number to hypergraphs is devel-oped. Circular colourings of graphs and hypergraphs are first discussed and it is shown that the circular chromatic number of a graph is the same regard-less of whether the hypergraph or graph definition is used. After presenting a few basic results, some examples of circular chromatic numbers of various families of hypergraphs are given. Subsequently, the concepts of the star chromatic number and the arc chromatic number are introduced. Specif?ically, both numbers are shown to be equivalent to the circular chromatic number. Finally the relationship between the imbalance of a hypergraph and the circular chromatic number is explored and a classical result of Minty is deduced.
Download or read book The Circular Chromatic Number of Hypergraphs written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalization of the circular chromatic number to hypergraphs is devel-oped. Circular colourings of graphs and hypergraphs are first discussed and it is shown that the circular chromatic number of a graph is the same regard-less of whether the hypergraph or graph definition is used. After presenting a few basic results, some examples of circular chromatic numbers of various families of hypergraphs are given. Subsequently, the concepts of the star chromatic number and the arc chromatic number are introduced. Specifically, both numbers are shown to be equivalent to the circular chromatic number. Finally the relationship between the imbalance of a hypergraph and the circular chromatic number is explored and a classical result of Minty is deduced.
Download or read book Chromatic Polynomials and Chromaticity of Graphs written by F. M. Dong and published by World Scientific. This book was released on 2005 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book into three main parts, the authors take readers from the rudiments of chromatic polynomials to more complex topics: the chromatic equivalence classes of graphs and the zeros and inequalities of chromatic polynomials. The early material is well suited to a graduate level course while the latter parts will be an invaluable resource for postgraduate students and researchers in combinatorics and graph theory."--BOOK JACKET.
Download or read book Tensor Analysis written by Liqun Qi and published by SIAM. This book was released on 2017-04-19 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors.
Download or read book On Some Conjectures on the Chromatic Index of Hypergraphs written by Tomaś.̆ Dvorăḱ and published by . This book was released on 1993 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discussiones Mathematicae written by and published by . This book was released on 2000 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Upper Chromatic Number and Chromatic Polynomials of Some Mixed Hypergraphs written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Behavior of the Chromatic Index for Hypergraphs written by International Business Machines Corporation. Research Division and published by . This book was released on 1987 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Chromatic Polynomials of Hypergraphs and Mixed Hypergraphs written by Ruixue Zhang and published by . This book was released on 2020 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Coloring Nearly disjoint Hypergraphs with N o n Colors written by DIMACS (Group) and published by . This book was released on 1990 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "It is shown that the chromatic index of a nearly- disjoint hypergraph on n vertices is at most n+o(n). This is an approximate version of the well-known Conjecture of Erdös, Faber and Lovász stating that the chromatic index is at most n."
Download or read book Chromatic Polynomials and Chromaticity of Graphs written by F. M. Dong and published by World Scientific. This book was released on 2005 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to comprehensively cover chromatic polynomialsof graphs. It includes most of the known results and unsolved problemsin the area of chromatic polynomials. Dividing the book into threemain parts, the authors take readers from the rudiments of chromaticpolynomials to more complex topics: the chromatic equivalence classesof graphs and the zeros and inequalities of chromatic polynomials.
Download or read book Graphs Hypergraphs and Matroids II written by Mieczysław Borowiecki and published by . This book was released on 1987 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
