This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973.This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation.This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation.This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation.Preface; 1. Perfect codes and distance-transitive graphs N. Biggs; 2. Generalisation of Fisher's inequality to fields with more than one element P. J. Cameron; 3. On balanced arrays D. V. Chopra; 4. Positions in Room squares R. L. Constable; 5. Analogues of Heawood's theorem R. J. Cook; 6. Cut-set lattices of graphs F. Escalante; 7. On the chromatic index of a graph, II. S. Fiorini and R. J. Wilson; 8. On a theorem of R. A. Liebler A. Gardiner; 9. Outerthickness and outercoarseness of graphs R. K. Guy; 10. Graphs with homeomorphically irreducible spanning trees A. Hill; 11. A note on embedding latin rectangles A. J. W. Hilton; 12. Some results in semi-stable graphs D. A. Holton; 13. Hereditary properties and P-chromatic numbers R. P. Jones; 14. Some probllc<