## Degeneracy graphs and the neighbourhood problem |

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### Contents

Appendices | 101 |

B Basic concepts of graph theory | 107 |

Flowcharts | 119 |

Copyright | |

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### Common terms and phrases

algorithm Appendix basic-index-sets basis set BLP problems called column complete basic solution connected convex polyhedral set convex polytope corresponding degeneracy Definition dege degeneracy degree degenerate vertex denoted Edited exactly example existence form of Tab G(Xe Gmax go to Step graph G index set isolated node laid degeneracy tableaux Lemma linear inequalities linear programming minimally laid degeneracy multiple degeneracy N-minimal tree N-tree method neighbourhood problem neighbouring vertices neracy node of G node set nodes of degeneracy nondegenerate nonzero elements number of edges number of nodes o-degenerate one-element set optimal solution oxn-degeneracy graphs perturbation pivot element pivot step pivot tableau positive degeneracy graph Remark representation graph G(X respect satisfies the N-condition Section simplex algorithm solution set solving the neighbourhood starting node starting tableau subgraph subroutine tableau associated tableau density tableau of type transition degree transition node transition set tree node TREE-solution trees of G Umax Umin vertex x