27th Conference of the International Linear Algebra Society (ILAS 2026)

Leaky Forcing of Unicyclic Graphs

May 20, 2026, 10:45 AM

25m

Goodwin Hall 155 (Virginia Tech)

Minisymposium Talk The Inverse Eigenvalue Problem of a Graph and Zero Forcing The Inverse Eigenvalue Problem of a Graph and Zero Forcing

Speaker

Carolyn Reinhart (Swarthmore College)

Description

Zero forcing is a graph coloring process in which a set of initially blue vertices force the remaining vertices in the graph to be colored blue after repeated applications of a color change rule. Leaky forcing is a fault-tolerant variant of zero forcing in which some set of $\ell$ vertices, called leaks, are forbidden from forcing. The $\ell$-leaky forcing number is the size of the smallest set of initially blue vertices for which the graph is successfully forced despite the placement of $\ell$ leaks. In this talk, we will characterize the $\ell$-leaky forcing number for unicyclic graphs.