Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem. Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise. TOC:Foreword.- Avant-propos.- Contributing Authors.- Preface.- Variable Neighborhood Search for Extremal Graphs - XI Bounds on Algebraic Connectivity.- Problems and Results on Geometric Patterns.- Data Depth and Maximum Feasible Subsystems.- The Maximum Independent Set Problem and Augmenting Graphs.- Interior Point and Semidefinite Approaches in Combinatorial Optimization.- Balancing Mixed-Model Supply Chains.- Bilevel Programming: A Combinatorial Perspective.- Visualizing, Finding and Packing Dijoins.- Hypergraph Coloring by Bichromatic Exchanges.
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