Description 
1 online resource (217 pages) 
Series 
London Mathematical Society lecture note series ; 141 

London Mathematical Society lecture note series ; 141.

Contents 
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 HAMADASACHAR 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 Incompleteblock 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; FLAGTRANSITIVE 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, kout 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 tDESIGNS; 1. INTRODUCTION; 2. PRELIMINARY DEFINITIONS AND RESULTS 
Summary 
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 
Bibliography 
Includes bibliographical references 
Notes 
Print version record 
Subject 
Combinatorial analysis  Congresses


MATHEMATICS  General.


Combinatorial analysis


CombinatÃ³ria (congressos)


Analyse combinatoire  CongrÃ¨s.

Genre/Form 
Conference papers and proceedings

Form 
Electronic book

Author 
Siemons, Johannes

ISBN 
9781461938231 

1461938236 

9781107359949 

1107359945 

9781107387270 

1107387272 
