Surveys in Combinatorics, 1989

Invited Papers at the Twelfth British Combinatorial Conference

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Paperback | 2 October 1989

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The invited lectures given at the 12th British Combinatorial Conference are contained in this volume. The lectures survey many areas of current research activity in combinatorics and its applications, including graph theory, designs and probabilistic graphs. This book provides a valuable survey for the present status of knowledge in combinatorics for mathematicians, computer scientists and engineers and research workers in combinatorics.

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On the theory of designs
Introduction	p. 1
The code and the hull of a design	p. 4
The hull of an affine plane	p. 7
The Hamada-Sachar conjecture and translation planes	p. 9
Derivations	p. 16
Conclusions	p. 17
Admissible parameters for designs	p. 17
References	p. 20
Designs: mappings between structured sets
Structured sets	p. 22
Fractional factorials	p. 24
Factorial structures	p. 26
Strata	p. 30
Incomplete-block designs	p. 34
General balance	p. 37
Randomization	p. 41
Neighbour designs	p. 44
References	p. 45
Developments based on Rado's dissertation 'Studien zur
Kombinatorik'
Partition regular matrices	p. 52
(m,p,c)-sets	p. 56
Combinatorial lines and parameter sets	p. 60
Graphs with arithmetic structure	p. 65
Canonizing Ramsey theory	p. 67
References	p. 71
Designs and automorphism groups
Introduction	p. 75
Flag-transitive 2-(v,k,1) designs	p. 77
Two applications	p. 80
References	p. 82
On matchings and Hamiltonian cycles in random graphs
Introduction	p. 84
"Proofs" of theorems 1.1 and 1.2	p. 86
Generalisations	p. 90
Regular graphs, k-out and planar maps	p. 96
Algorithmic aspects	p. 99
Digraphs	p. 106
Open problems	p. 108
References	p. 110
Decompositions of complete bipartite graphs
Setting the stage	p. 115
A small detour. Some connections with latin squares	p. 120
The Ringel conjecture	p. 124
The Oberwolfach problem	p. 133
Main results	p. 135
References	p. 146
On the method of bounded differences
Introduction	p. 148
Colouring random graphs - before and after	p. 150
Colouring random graphs - proofs	p. 153
Martingales	p. 158
Inequalities for bounded independent summands	p. 161
Inequalities for bounded martingale difference sequences	p. 165
Isoperimetric inequalities for graphs	p. 169
Applications in operational research and computer science	p. 178
Concluding remarks	p. 183
References	p. 184
On the use of regular arrays in the construction of t-designs
Introduction	p. 189
Preliminary definitions and results	p. 189
Completing a regular (L)ES([lambda];t,t+1,v) to an (L)S([lambda]t,t+1,v+t)	p. 194
Direct products	p. 197
Repetition-trivial arrays and t-trivial designs	p. 198
Other applications of regular ES([lambda];t,t+1,v)	p. 202
References	p. 206
The 'Snake Oil' method for proving combinatorial identities
The 'Snake Oil' method	p. 208
Several examples	p. 210
WZ Pairs	p. 216
References	p. 217
Table of Contents provided by Syndetics. All Rights Reserved.

Surveys in Combinatorics, 1989

Invited Papers at the Twelfth British Combinatorial Conference

At a Glance

Paperback

Shipping

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