A tribute to Torrence Parsons

Abstract

I first met my friend and co-worker Tory Parsons in the autumn of 1972 when I first visited Penn State University . We had several long mathematical discussions and I visited him at his home and met his boss and epsilons which, if I remember right, were quite small at that time . We shared a common interest in graph theory in general and in theory in particular . He wrote a nice survey article, Ramsey Graph Theory, in selected topics of graph theory in 1979. In our work with Faudree, Rousseau and Schelp we several times used his results . Besides theory he worked on long cycles, universal graphs and block designs . He shared with me his love of traveling and his liking of collaboration . He liked to give lectures at meetings -it is very sad that he died just before his lecture tour to Australia and New Zealand. (He was supposed to lecture in May, 1987 to the Australian and New Zealand Mathematical Society) . In 1985 he lectured on graph theory in Dubrovnick, Yugoslavia . He visited many of the meetings in the U .S . and our joint paper was started at such a meeting . He was also very fond of outdoor activities, perhaps he overdid this, since it seems that he died after a marathon run of ventricular fabrillation . In any case, his untimely death is a great loss to Mathematics, his many friends, and his family . Now I write a few words about our joint paper which will soon appear in the European Journal of Combinatorics (Intersection graphs for families of balls in R (P. Erdos, C . Godsil, S . G. Krantz and T. Parsons) . Let F be the family of balls in n-dimensional Euclidean R. Denote by G the graphs which can be represented as the interaction graphs of sets in F„ . By G ., we denote the set of graphs which can be represented by balls in F so that B, and B, are adjacent if