Tuesday, April 21th, 2026
2:00pm – 2:50pm
Stratton Hall 311
Speaker: Ralihe Villagran, WPI
Title: On zero-forcing, the minimum rank, and the critical ideals of Block and threshold graphs
Abstract: The zero-forcing number yields a combinatorial lower bound for the minimum rank of a graph. Carlos Alfaro and Jephian Lin studied the relation of both parameters with the algebraic co-rank (cr), which is defined as the largest i such that the i-th critical ideal is trivial. They proved that the min. rank is at most the alg. co-rank for any algebraically closed field, and conjectured that the same was true over the real numbers. We present their results on the relationship between these parameters and expand on previously known families where the gaps between them vanish. Finally, we study the three parameters for the family of threshold graphs.