The combinatorial workshop ‘Some Trends in Discrete Mathematics’ was held in Matrahaza, Hungary, from 22 to 28 October 1995. The aim of the workshop was to expose connections between distant parts of combinatorial mathematics, such as pure combinatorics, graph theory, combinatorial number theory and random graphs, by bringing together researchers from diverse fields. To emphasize the workshop character of this meeting, we invited many distinguished mathematicians but asked only ten of them to give lectures. (Unfortunately, illness prevented Claude Berge from attending the meeting.) There were no contributed talks, but the lectures were followed by long discussions involving all the participants: these sessions played a crucial role in the success of the workshop. A tangible result of these evening discussions is the Cameron–Erdős paper in this volume.

A highlight of the volume is the paper Paul Erdős was writing on the eve of his sudden death in Warsaw on 20 September, 1996. This paper had no title and, except for light editing, this very special manuscript is published as he left it. The other eight papers of this issue are surveys and research papers written by the invited speakers and their collaborators.

We want to thank all the participants of the workshop for their contribution to its success. We are also grateful to DIMANET and its main coordinator, Professor Walter Deuber, for providing the financial support that made the workshop possible. We wish to express our sincere thanks to Béla Bollobás who made it possible to publish these papers in a special issue of Combinatorics, Probability and Computing.