Dr. John Lattanzio of the Mathematics Department had his manuscript, “Partition Types,” accepted for publication in the Journal of Combinatorial Mathematics and Combinatorial Computing.
This article combines the areas of theoretical graph theory and abstract algebra. This combination of mathematical areas gives fascinating results concerning the partitions of V(G) as they relate to a forty-two-year unsolved problem in graph theory posed by Erdős and Lovász.
In this article, for a graph G having chromatic number k, Dr. Lattanzio defines an equivalence relation on the set X of all proper vertex k-colorings of G. This leads naturally to an equivalence relation on the set P of all partitions of V(G) into k independent subsets of color classes. He then investigates the notion of a partition type and the algebra of types.
