## Studies in graph theory, Part 1 |

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### Contents

TRANSVERSAL THEORY AND GRAPHS | 23 |

ON THE SHORTEST ROUTE | 89 |

FLOW NETWORKS AND COMBINATORIAL | 139 |

Copyright | |

2 other sections not shown

### Common terms and phrases

a-perfect adjacency matrix adjacent bipartite graph black squares clique color combinatorial comparability graph connected components consider contains Corollary cover cut separating cycle D. R. Fulkerson defined denoted distinct representatives dominos Duffin electrical networks equal exists families of sets family 21 family of subsets finite family flow problem following theorem graph G graph theory Hence independent set induced subgraph inequality infinite integer interval graph joint resistance junctor l)/2 squares Lemma Let G linear matching in G matching which matches Math matrix maximal flow maximal set maximum cardinality maximum number minimal cost flow minimal cut minimum network flow ohms partial transversal path perfect graph proof pruned board rank function red squares resistor boxes satisfies separating set series-parallel set in Mx set of nodes shortest chain shown in Figure spanning tree stable set subgraph Suppose synthesized terminal Theorem 1.1 transversal matroid transversal of 21 transversal theory unimodular vector vertices