ABSTRACT
Throughout the years since the Southeastern International Conference on Combinatorics, Graph Theory and Computing began, there has been a constant presence of talks on graph decompositions. Indeed, the development of in-depth study of such structures, and growth of interest in graph decompositions, was greatly enhanced by the opportunity to meet and discuss such issues at this conference. In this paper, it is shown that the growth continues by focusing on a very interesting parameter that has appeared off and on over the past 50 years as our techniques become deeper and more suitable to its study.
