## Network OptimizationTopics include optimal branching problems, trans-shipment problems, shortest path problems, minimum cost flow problems, maximum flow problems, matching in bipartite and nonbipartite graphs, and applications to combinatorics. |

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### Contents

Transshipment problems | 40 |

Shortest path problems | 89 |

Minimum cost flow problems | 122 |

Matchings in graphs | 194 |

232 | |

245 | |

### Common terms and phrases

acyclic algorithm artificial arc augmenting path backward arc bipartite graph blossom capacitated column complete graph components construct corresponding cost matrix cost vector critical graph current flow cutset define delete digraph G Dilworth's theorem directed path elements Eulerian circuit Example exposed vertex feasible flow feasible solution feasible tree solution flow augmenting path flow vector forward arc go to step graph G implies incidence matrix integer intermediate vertex iteration labeled left vertex Let G lower bound matched edge max-flow min-cut theorem maximum cardinality matching maximum flow problem maximum flow value maximum weight branching minimal spanning tree minimum cut minimum weight arborescence network G network shown nonnegative number of vertices odd cycle optimal assignment optimal Hamiltonian cycle optimal solution poset procedure profitable arc set of vertices shortest path sink solve Steiner tree subgraph subset subtours supply-demand vector transshipment problem undirected graph unique upper bound weight matrix