Charlie with Gravensteen behind him (Ghent, Belgium).
This conference will celebrate the 65th birthday of Professor Charles J. Colbourn. It is also an opportunity to recognize Professor Colbourn’s contributions to combinatorial design theory and application-oriented research in communications, networking, software testing, and bioinformatics.
The long lists of accomplishments that follow are a testament to Professor Colbourn’s energy. However the real story lies in the quality and impact of his work. The regularity with which he is a key player in the solution of long-standing open problems is striking. Just ten examples are given here:
- in 1981, the solution of a 1938 problem of Peltesohn on cyclic triple systems;
- in 1982, determining the complexity of design isomorphism, solving a 1956 problem of Hall;
- in 1983, finding the complexity of completing Latin squares, solving a 1965 problem of Fulkerson;
- in 1986, orienting triple systems, solving a 1972 problem of Mendelsohn;
- in 1988, the characterization of Steiner complexes, solving a 1935 problem of Whitney and a 1962 problem of Lehman;
- in 1992, determining support sizes of triple systems, the solution of a 1972 problem of Hedayat;
- in 1994, the solution of O’Shaughnessy’s 1968 problem on existence of orthogonal Steiner triple systems;
- in 1996, the solution of one of Erdös’s celebrated problems from 1976, the existence of anti-Pasch triple systems;
- in 2001, the solution of a problem dating back to Kirkman in 1847 on doubly resolvable designs;
- and in 2002, the first improvement in 25 years on a 1782 problem of Euler on mutually orthogonal Latin squares.
Perhaps more remarkable is the frequency with which Professor Colbourn writes the seminal paper on a new topic, opening a new and unexpected line of research. For example,
- his 1981 work on 2-trees underlies a substantial literature on “isolated failure immune networks;”
- his 1990 work on unit disk graphs has found wide application in mobile and wireless networking;
- his 1992 formulation of the Brown-Colbourn conjecture on zeroes of reliability polynomials led to novel bounds for network reliability but has spawned research in algebraic geometry, combinatorial topology, and spin glass models in physics as well as combinatorics and algorithms;
- his 1998 work on nonadaptive group testing is applied in bioinformatics;
- his 1999 work on orthogonal Latin squares and permutation codes is underpinning new techniques in powerline communication;
- and his 2007 work on locating arrays has the potential to revolutionize experimental design.
These lists are just some highlights of a deep and broad record of achievement in research. Indeed the statement from the Institute for Combinatorics and Its Applications awarding Professor Colbourn the Euler Medal for Lifetime Research Achievement states “To compile a list of his citations would be an almost impossible task – the level of his overall activity has been phenomenal. He ranks among the top combinatorial design theorists.”