Combinatorics : proceedings of the Eighth British Combinatorial Conference, University College, Swansea, 1981 / edited by H.N.V. Temperley.

Includes bibliographical references.

Print version record.

The articles collected here are the texts of the invited lectures given at the Eighth British Combinatorial Conference held at University College, Swansea. The contributions reflect the scope and breadth of application of combinatorics, and are up-to-date reviews by mathematicians engaged in current research. This volume will be of use to all those interested in combinatorial ideas, whether they be mathematicians, scientists or engineers concerned with the growing number of applications.

Cover; Title; Copyright; Contents; Preface; 1. Resonance and reconstruction; SUMMARY; 1. INTERACTION MODELS; 2. THE ALGEBRA OF GRAPH TYPES; 3. RECONSTRUCTION; 4. PARTITION FUNCTIONS FOR INFINITE GRAPHS; REFERENCES; 2. Symmetry conditions in graphs; INTRODUCTION; EXAMPLE I; EXAMPLES IIA; EXAMPLE IIB; EXAMPLES IIC; EXAMPLES III; REFERENCES; 3. Extremal hypergraph problems; II. A CLASSICAL RESULT; III. RECENT RESULTS; IV. SOME OPEN QUESTIONS; REFERENCES; 4. Connectivity and edge-connectivity infinite graphs; I LOCAL CONNECTIVITY; II GLOBAL CONNECTIVITY

Ill CERTAIN CONFIGURATIONS IN n-CONNECTED GRAPHSIV EXTREMAL CONNECTIVITY PROBLEMS; REFERENCES; 5. Partition theory and its application; 1 Introduction; 2 Sample results; 3 Applications to category theory; 4 Applications to logic; 5 Applications to ultrafilters; 6 Applications to algebra; 7 Applications to partitions of integers; 8 Selective theorems; 9 Remarks on infinite sets and topological spaces; 10 Concluding remarks; References; 6. Strongly regular graphs; 1. INTRODUCTION; 2. DEFINITIONS; 3. ADJACENCY MATRICES; 4. ARITHMETIC; 5. THE ADJACENCY ALGEBRA; 6. THE ABSOLUTE BOUND

7. EXTREMAL STRONGLY REGULAR GRAPHS8. SWITCHING; 9. TWO EXAMPLES; REFERENCES; 7. Geometries in finite projective and affine spaces; 1. SOME INTERESTING FINITE GEOMETRIES; 2. EMBEDDING IN FINITE PROJECTIVE SPACES; 3. EMBEDDING IN FINITE AFFINE SPACES; REFERENCES; 8. Long cycles in digraphs with constraints on the degrees; INTRODUCTION; TERMINOLOGY; LONG CYCLES IN DIGRAPHS; REFERENCES; 9. Colouring problems and matroids; 1. INTRODUCTION; 2. TUTTE-GROTHENDIECK INVARIANTS; 3. THE FLOW POLYNOMIAL; 4. THE COLOURING PROBLEM AND PROJECTIVE GEOMETRY; 5. SEYMOUR'S THEORY OF SPLITTERS

7. CONCLUSIONS: SOME OPEN PROBLEMSREFERENCES; Index

English.

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