Random Graphs

Random Graphs '85

Covering a wide range of Random Graphs subjects, this volume examines series-parallel networks, properties of random subgraphs of the n-cube, random binary and recursive trees, random digraphs, induced subgraphs and spanning trees in random graphs as well as matchings, hamiltonian cycles and closure in such structures. Papers in this collection also illustrate various aspects of percolation theory and its applications, properties of random lattices and random walks on such graphs, random allocation schemes, pseudo-random graphs and reliability of planar networks. Several open problems that were presented during a special session at the Seminar are also included at the end of the volume.

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Published: December 1987

Imprint: North-holland

ISBN: 978-0-444-70265-4

Contents

  • A Variant of Banach's Match Box Problem (S. Berg). The Sensitivity of Expected Spanning Trees in Anisotropic Random Graphs (J.E. Cohen). On the Strength of Connectivity of Random Subgraphs of the n-Cube (M.E. Dyer, A.M. Frieze and L.R. Foulds). Connectedness and Connectivity in Percolation Theory (J.W. Essam). Hamiltonian Closure in Random Graphs (J. Gimbel, D. Kurtz, L. Lesniak, E.R. Scheinerman and J.C. Wierman). Long Paths and Cycles in a Random Lattice (G.R. Grimmett). The Distribution of the Number of Empty Cells in a Generalized Random Allocation Scheme (B. Harris, M. Marden and C.J. Park). Random Self-Avoiding Walks in Some One-Dimensional Lattices (S. Janson). On a Random Digraph (J. Jaworski and I.H. Smit). Additive Weights of Non-Regularly Distributed Trees (R. Kemp). A Tree Enumeration Problem Involving the Asymptotics of the ``Diagonals'' of a Power Series (P. Kirschenhofer). On Matchings and Hamiltonian Cycles in Subgraphs of Random Graphs (T. Łuczak). General Percolation and Oriented Matroids (C. McDiarmid). Some Enumerative Results on Series-Parallel Networks (J.W. Moon). Unsolved Problems in the Theory of Random Graphs (E.M. Palmer). Some Recent Results on the Register Function of a Binary Tree (H. Prodinger). Bounds for All-Terminal Reliability in Planar Networks (A. Ramesh, M.O. Ball and C.J. Colbourn). Induced Subgraphs in a Random Graph (A. Ruciński). On a Nonuniform Random Recursive Tree (J. Szymański). Pseudo-Random Graphs (A. Thomason). On the Independence Number of Random Subgraphs of the n-Cube (K. Weber). Directed Site Percolation and Dual Filling Models (J.C. Wierman). Open Problems.

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