Event time:
Thursday, February 22, 2018 - 4:00pm to 5:00pm
Speaker:
Karen Collins
Speaker affiliation:
Wesleyan University
Event description:
A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk discovered the following interesting counting fact: unlabeled, unbalanced split graphs on n vertices can be placed into a bijection with all unlabeled split graphs on n-1 or fewer vertices (the Balance Theorem). Ourmotivation for considering split graphs comes from their extremal properties related to the Nordhaus-Gaddam Theorem for the distinguishing chromatic number. In this talk, we will discuss these connections and translations of the Balance Theorem to different combinatorial settings