## Algorithmic Aspects of CombinatoricsAlgorithmic Aspects of Combinatorics |

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### Contents

1 | |

Chapter 2 Which spheres are shellable? | 33 |

Chapter 3 A representation of 2dimensional pseudomanifolds and its use in the design of a lineartime shelling algorithm | 53 |

Chapter 4 An analysis of the greedy heuristic for independence systems | 65 |

Chapter 5 Sequencing jobs to minimize total weighted completion time subject to precedence constraints ... | 75 |

Chapter 6 Subtree isomorphism in On52 | 91 |

Chapter 7 Every one a winner or How to avoid isomorphism search when cataloguing combinatorial configurations | 107 |

Chapter 8 Complexity of monotone networks for computing conjunctions | 121 |

Chapter 12 An inequality on binomial coefficients | 155 |

Chapter 13 On the edgecoloring property for the closure of the complete hypergraphs | 161 |

Chapter 14 Steiner trees for ladders | 173 |

Chapter 15 Local unimodularity in the matching polytope | 201 |

Chapter 16 The Dilworth number of a graph | 211 |

Chapter 17 Biased positional games | 221 |

Chapter 18 A characterization of pseudoaffine designs and their relation to a problem of Cordes ... | 231 |

Chapter 19 Research Problems | 239 |

Chapter 9 A unified setting for selection algorithms II | 135 |

Chapter 10 Algorithms and extremal problems for equipartite colorings in graphs and hypergraphs abstract ... | 149 |

Chapter 11 Two results concerning multicoloring | 151 |

Between a rock and a hard place? abstract | 245 |

### Common terms and phrases

3-class association schemes 3-manifolds adjacency matrix association schemes augmenting operation automorphism backtracking BIBD bipartite matching problem Boolean Breaker canonical claim columns combinatorial complete conﬁgurations construction contains convex corresponding d-sphere deﬁned deﬁnition denote determined digraph edge-coloring edge-coloring property edges elements exists facets Fact ﬁnd ﬁnite ﬁrst follows full tree component function graph coloring graph G Graph Theory Hence hypergraph independence system integer intersection Latin square Lemma length limb imbedding matrix limb imbedding submatrix linear lower bound Maker Math matroids maximal maximum bipartite matching minimal minimum number minimum Steiner tree monotone network n-set network for computing North-Holland Publishing Company NP-complete obtained orderly algorithm p-maximal initial set pair parameters partial shelling partition path polytopes Proof pseudomanifold result rooted tree satisﬁes series parallel shellable solution speciﬁc split graph Steiner point strongly regular graphs subgraphs subtree isomorphism Theorem Topology unimodular vector vertex vicinal preorder