Surveys in combinatorics, 1989 : [invited papers for the Twelfth British Combinatorial Conference] / edited by Johannes Siemons.

Includes bibliographical references.

Print version record.

This volume contains the invited lectures given at the Twelfth British Combinatorical Conference. The lectures survey the many areas of current research activity in combinatorics and its applications, including graph theory, designs, and probabilistic graphs. This book provides a valuable survey of the present status of knowledge in combinatorics for mathematicians, computer scientists and engineers.

Cover; Series Page; Title; Copyright; PREFACE; CONTENTS; On the theory of designs; INTRODUCTION; THE CODE AND THE HULL OF A DESIGN; THE HULL OF AN AFFINE PLANE; THE HAMADA-SACHAR CONJECTURE AND TRANSLATION PLANES; DERIVATIONS; CONCLUSION; APPENDIX; ADMISSIBLE PARAMETERS FOR DESIGNS; REFERENCES; Designs: mappings between structured sets; 1 Structured sets; 2 Fractional factorials; 3 Factorial structures; 4 Strata; 5 Incomplete-block designs; 6 General balance; 7 Randomization; 8 Neighbour designs; References; DEVELOPMENTS BASED ON RADO'S DISSERTATION: ""Studien zur Kombinatorik""

I. PARTITION REGULAR MATRICESII. (m, p, c)-SETS; III. COMBINATORIAL LINES AND PARAMETER SETS; IV. GRAPHS WITH ARITHMETIC STRUCTURE; V. CANONIZING RAMSEY THEORY; References; DESIGNS AND AUTOMORPHISM GROUPS; INTRODUCTION; FLAG-TRANSITIVE 2-(v, k, l) DESIGNS; TWO APPLICATIONS; REFERENCES; ON MATCHINGS AND HAMILTON CYCLES IN RANDOM GRAPHS; 1. Introduction; 2. ""Proofs"" of Theorems 1.1 and 1.2; 3. Generalisations; 4. Regular Graphs, k-out and Planar Maps; 5. Algorithmic Aspects; Weighted Problems; 6. Digraphs; 7. Open Problems; References; Decompositions of complete bipartite graphs

0. Setting the stage1. A small detour. Some connections with latin squares; 2. The Ringel conjecture; 3. The Oberwolfach problem; 4. Main results; References; ON THE METHOD OF BOUNDED DIFFERENCES; 1 Introduction; 2 Colouring random graphs -- before and after; 3 Colouring random graphs -- proofs; (a) General lemmas; (b) Concentration of X[Gn, p]; (c) Stable sets in Gn, p; (d) Colouring Gnp; (e) Stability number of sparse random graphs; 4 Martingales; 5 Inequalities for bounded independent summands; (a) Results; (b) Proofs; 6 Inequalities for bounded martingale difference sequences

(A) Results(b) Proofs; (c) Inequalities for maxima; 7 Isoperimetiic inequalities for graphs; (a) General results; (b) Exact isoperimetric inequalities; (c) Two results of Alon and Milman; (d) Monotonic functions; 8 Applications in operational research and computer science; (a) Bin packing; (b) Knapsack problems; (c) Travelling salesman problem; (d) Minimum spanning trees; (e) Second eigenvalue of random regular graphs; (f) Heap building; 9 Concluding Remarks; References; ON THE USE OF REGULAR ARRAYS IN THE CONSTRUCTION OF t-DESIGNS; 1. INTRODUCTION; 2. PRELIMINARY DEFINITIONS AND RESULTS

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