Graphs, Algorithms, and Optimization - Info and Reading Options

Google Books:

Graph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NP-Completeness and polynomial reduction. A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. The book covers major areas of graph theory including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently. The book also provides coverage on algorithm complexity and efficiency, NP-completeness, linear optimization, and linear programming and its relationship to graph algorithms. Written in an accessible and informal style, this work covers nearly all areas of graph theory. Graphs, Algorithms, and Optimization provides a modern discussion of graph theory applicable to mathematics, computer science, and crossover applications.

Open Data:

GRAPHS AND THEIR COMPLEMENTS -- Degree sequences -- Analysis -- PATHS AND WALKS -- Complexity -- Walks -- The shortest path problem -- Weighted graphs and Dijkstra's algorithm -- Data structures -- Floyd's algorithm -- SOME SPECIAL CLASSES OF GRAPHS -- Bipartite graphs -- Line graphs -- Moore graphs -- Euler tours -- TREES AND CYCLES -- Fundamental -- Co-trees and bonds -- Spanning tree algorithms -- THE STRUCTURE OF TREES -- Non-rooted -- Read's tree encoding algorithm -- Generating rooted trees -- Generating non-rooted trees -- Pr�fer sequences -- Spanning trees -- The matrix-tree theorem -- CONNECTIVITY -- Blocks -- Finding the blocks of a graph -- The depth-first search -- ALTERNATING PATHS AND MATCHINGS -- The Hungarian algorithm -- Perfect matchings and 1-factorizations -- The subgraph problem -- Coverings in bipartite graphs -- Tutte's theorem -- NETWORK FLOWS -- Introduction -- The Ford-Fulkerson algorithm -- Matchings and flows -- Menger's theorems -- Disjoint paths and separating sets -- Notes -- HAMILTON CYCLES -- The crossover algorithm -- The Hamilton closure -- The extended multi-path algorithm -- The traveling salesman problem -- The TSP -- Christofides' algorithm -- DIGRAPHS -- Activity graphs, Critical paths -- Topological order -- Strong components -- An application to fabrics -- Tournaments -- Satisfiability -- GRAPH COLORINGS -- Cliques -- Mycielski's construction -- Critical graphs -- Chromatic polynomials -- Edge colorings -- NP-completeness -- PLANAR GRAPHS -- Jordan curves -- Graph minors -- Subdivisions -- Euler's formula -- Rotation systems -- Dual graphs -- Platonic solids -- Triangulations -- The sphere -- 5 Whitney's theorem -- Medial digraphs -- The 4-color problem -- Straight line drawings -- Kuratowski's theorem -- The Hopcroft-Tarjan Algorithm -- GRAPHS AND SURFACES -- Surfaces -- Graph embeddings -- Graphs on the torus -- Graphs on the projective plane -- LINEAR PROGRAMMING -- The simplex algorithm -- Cycling -- THE PRIMAL-DUAL ALGORITHM -- Alternate form of the primal and its dual -- Geometric interpretation -- Complementary slackness -- The dual of the shortest path problem -- The primal-dual algorithm -- DISCRETE LINEAR PROGRAMMING -- Backtracking -- Branch and bound -- Unimodular matrices -- BIBLIOGRAPHY -- INDEX

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