Brian Alspach, Professor Emeritus

Ph.D. Mathematics · UC Santa Barbara · 1966

Ph: 306-585-4886 | Fax: 306-585-4020


Research Interest

My interests are graph theory and its applications. One major direction deals with coverings and decompositions. In particular, decompositions of graphs into paths, cycles and trees, covering weighted graphs with cycles, 1-factorizations and general isomorphic factorizations are being studied. Such factorizations can be and have been utilized in solving scheduling problems. Another major direction deals with the existence of Hamilton cycles and paths in vertex-trasitive graphs. Such problems are of interest in interconnection networks and parallel architectures. Another area of interest is the interaction of graph theory and design theory. Particular instances of this are the study of orthogonal factorizations of graphs and the study of matching designs. Cayley graphs is another major topic in which I am interested. They have become an extremely active area of research because of their interest in network probelms. Circulant graphs and digraphs is a particular family of Cayley graphs in which I am interested. Circulant graphs have interesting interactions with group theory because of isomorphism questions. Circulant graphs also appear in many graph-theoretic settings.