Georgia Institute of Technology College of Sciences

The map coloring problem is one of the major catalysts of the tremendous development of graph theory. It was observed by Tutte that the problem of the face-coloring of an planar graph can be formulated in terms of integer flows of the graph. Since then the topic of integer flow has been one of the most attractive in graph theory. Tutte had three famous fascinating flow conjectures: the 3-flow conjecture, the 4-flow conjecture and the 5-flow conjecture. There are some partial results for these three conjectures. But in general, all these 3 conjectures are open. Group connectivity is a generalization of integer flow of graphs. It provides us with contractible flow configurations which play an important role in reducing the graph size for integer flow problems, it is also related to all generalized Tutte orientations of graphs. In this talk, I will present an introduction and survey on group connectivity of graphs as well as some open problems in this field.