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. Colorings were originally introduced by C. J. Colbourn and A. Rosa, who considered block colorings of Steiner Triple Systems. Another important recent development in the study of equitable block-colorings is the formation of our understanding of the structure within such colorings. This chapter provides another setting where the method of amalgamations plays a useful role. The amalgamation approach has been successfully used in many graph decomposition results, especially when edge-colorings representing the decompositions are required to share the colors out fairly in quite a variety of ways.
