Graduate Seminar

Location:  RI 208

Speaker: Layne Burns

MSc Student supervised by Edward Doolittle and Shaun Fallat

Title:  Some Results on 1-Capacitated Graph Burning

 Abstract:

This seminar continues our investigation into the 1-capacitated graph burning process, \(\hat{b}_{1}(G)\), a variant of graph burning constrained by local neighbourhood capacity. Building on the foundational definitions, we focus on the relationship between this process, zero forcing, and graph throttling. We establish that \(\hat{b}_{1}(G)\) is bounded by the throttling number, \(th(G)\), and reframe the search for an optimal burning sequence as a geometric packing problem. While standard throttling minimizes the sum of resources and propagation time (effectively packing forcing chains into a rectangular domain), the 1-capacitated process requires packing these chains into a strict triangular capacity structure, defined by the limited growth rate of the fire. Finally, we introduce structural tools designed to assist our analysis of certain graph families, specifically addressing the impact of dominating vertices and the utility of the geometric dual graph.