Graduate Seminar

Location:  CL 305 and Live Stream

Speaker: Layne Burns

MSc Student supervised by Edward Doolittle and Shaun Fallat

Title:  Capacitated Graph Burning

 Zoom Link:  https://uregina-ca.zoom.us/j/92805435386?pwd=42pEMT2QL4b8W8bqIOr5Y39hln8bSI.1

Abstract:

The standard graph burning process provides a foundational model for analyzing network propagation by minimizing initial ignition sources. This seminar investigates two generalizations that introduce constraints on the spread of fire: the 1-capacitated burning process, \(\hat{b}_1(G)\), and the positive 1-capacitated burning process, \(\hat{b}_+(G)\). 

These variants enforce a 'capacity-lock' rule, defined by local neighbourhood conditions on the unburned vertex set. We formally develop these models and establish the structural hierarchy among all three burning processes. We then establish a connection between these capacitated burning numbers and the concepts of zero-forcing and positive zero-forcing.