## Graphs: Theory and AlgorithmsThis adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography. |

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### Contents

PREFACE xili | 1 |

TREES CUTSETS AND CIRCUITS | 31 |

EULERIAN AND HAMILTONIAN GRAPHS | 55 |

GRAPHS AND VECTOR SPACES | 72 |

DIRECTED GRAPHS | 97 |

MATRICES OF A GRAPH | 126 |

Graph | 155 |

PLANARITY AND DUALITY | 179 |

CONNECTIVITY AND MATCHING | 200 |

COVERING AND COLORING | 236 |

MATROIDS | 265 |

GRAPH ALGORITHMS | 306 |

FLOWS IN NETWORKS | 390 |

445 | |

451 | |

### Common terms and phrases

acyclic adjacent algorithm augmenting path back edge bipartite graph circuit of G circuit subspace cocircuit coloring computing connected graph Consider construct contains Corollary corresponding defined denote directed circuits directed graph directed path directed s-t path dual edge set edge-disjoint edge-induced subgraph edges incident edges of G electrical network elements end vertices equal Eulerian graph exists following theorem fundamental circuit fundamental cutset graph G graph of Fig graph theory Hence in-degree incidence matrix independent set induced subgraph labeling layered network Lemma length Let G matroid maximal maximum flow maximum matching n-vertex nonzero number of edges number of vertices paths in G planar graph problem Proof prove push result ring sum saturated self-loops shortest paths shown in Fig simple graph spanning tree strongly connected strongly connected component subgraph of G submatrix subset Suppose transitive closure transport network tree of G undirected vector space vertex set vertices of G weight spanning tree