## Congressus Numerantium, Volume 130 |

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### Contents

Parallel Generation of Random Trees and Connected Graphs | 7 |

Analysis of Partition Variance for the Number Partition Problem | 29 |

The Complexity of Toughness in Regular Graphs | 47 |

Copyright | |

10 other sections not shown

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### Common terms and phrases

1-tough adjacent Ahlswede-Zhang aj-stable algorithm BF binary bipartite graph blue vertex central vertex chains closed dominating walk color Combinatorial complete graph Computer CONGRESSUS NUMERANTIUM 130 conjecture connected graph construction Corollary cubic graphs cutset cycle d-nonadjacent in dom(T defined Definition denote digraph domination graph edges eigenvalues element error(BF exactly exists expander graphs Figure finite Goppa codes graph G Graph Theory Gray code Hamiltonian Hence independence number induced subgraph integer Intel Paragon isomorphic k-partition Koenig-Egervary graph Lemma length Let G loop LTks.s m-nonadjacent MasPar Mathematics MIMD nodes nonadjacent nontrivial NP-Complete NP-hard obtained optimal watchman's walk overflow pair parallel partition dimension path tournament perfect matching player processors prove psort PTCH(v Ramanujan graphs red vertex regular tournament resolving partition resp result round SIMD strictly fair subgraph of dom(T subsets subtournament triangles uniform central graphs V(Pi V(Qj vertex vertex set vertices Z-cyclic