Balanced and Unbalanced Split Graphs

November 22, 2019, 9:10 AM - 9:25 AM


The Heldrich Hotel & Conference Center

10 Livingston Avenue

New Brunswick, NJ 08901

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Ann Trenk, Wellesley College

A graph is a split graph if its vertex set can be partitioned into a clique and an independent set. A split graph is unbalanced if there exist two such partitions that are distinct. We discuss a variety of results about balanced and unbalanced split graphs, including showing that these classes can be recognized by their degree sequences and that all threshold graphs are unbalanced split graphs. This is joint work with Karen Collins, Wesleyan University.

Speaker Bio: Ann Trenk is Professor of Mathematics at Wellesley College. Her research interests lie in graph theory and partially ordered sets, with a particular emphasis on structured families of graphs, including interval graphs, perfect graphs, and tolerance graphs. Her work in this area led to the book, Tolerance Graphs, which she coauthored with Martin Golumbic. Trenk has taught high school students both as a full-time teacher and in summer programs, organized math enrichment activities for elementary school children, and has led a variety of outreach activities for K-12 teachers. She spent a sabbatical year at DIMACS and has taught in a range of DIMACS summer programs, including the Young Scholars Program for high school students, Leadership Program for K–12 teachers, and DIMACS Connect Institute to engage high school teachers in research topics in discrete mathematics.