2011. — 299 p.Introduction to Graph Theory. Graphs and digraphs. Subgraphs and other graph types. Representing graphs as matrices. Isomorphic graphs. New graphs from old. Common applications. Problems. Graph Algorithms. Representing graphs in a computer. Graph searching. Weights and distances. Dijkstra's algorithm. Bellman-Ford algorithm. Floyd-Roy-Warshall algorithm. Johnson's algorithm. Problems. Trees and Forests. De nitions and examples. Properties of trees. Minimum spanning trees. Binary trees. Human codes. Tree traversals. Problems. Tree Data Structures. Priority queues. Binary heaps. Binomial heaps. Binary search trees. AVL trees. Problems. Distance and Connectivity. Paths and distance. Vertex and edge connectivity. Menger's theorem. Whitney's Theorem. Centrality of a vertex. Network reliability. Problems. Optimal Graph Traversals. Eulerian graphs. Hamiltonian graphs. The Chinese Postman Problem. The Traveling Salesman Problem. Planar Graphs. Planarity and Euler's Formula. Kuratowski's Theorem. Planarity algorithms. Graph Coloring. Vertex coloring. Edge coloring. Applications of graph coloring. Network Flows. Flows and cuts. Ford-Fulkerson theorem. Edmonds and Karp's algorithm. Goldberg and Tarjan's algorithm. Random Graphs. Network statistics. Binomial random graph model. Erdos-Renyi model. Small-world networks. Scale-free networks. Problems. Graph Problems and Their LP Formulations. Maximum average degree. Traveling Salesman Problem. Edge-disjoint spanning trees. Steiner tree. Linear arboricity. H-minor.
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