Title: The Erdos-Lovasz Double-Critical Conjecture

Abstract: A simple, connected graph is said to be double-critical if removing any pair of adjacent vertices lowers the chromatic number of the graph by exactly two. In 1966, Paul Erdos and Laszlo Lovasz proposed the Double-Critical Conjecture which states that the complete graph is the only simple, connected graph that is a double-critical graph. This result has been proven when the chromatic number of a graph is less than six, but is still open for the other cases. In this talk, concepts and results related to this problem will be discussed.