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Atlantic Graph Theory Seminar

October 22, 2025 @ 3:30 pm - 4:30 pm

Date and Time: Wednesday, October 22, 3.40 pm Atlantic time
Speaker: Theodore (Teddy) Mishura, Toronto Metropolitan University
Title: Liminal burning the hypercube
 
Abstract: Liminal burning generalizes both the burning and cooling processes in graphs. In $k$-liminal burning, a Saboteur reveals $k$-sets of vertices in each round, and the Arsonist must choose sources only within these sets. The result is a two-player game with the corresponding optimization parameter $b_k$ called the $k$-liminal burning number. For $k = |V (G)|$, liminal burning is identical to burning, and for $k = 1$, liminal burning is identical to cooling. Here, we study the behavior of $k$-liminal burning on the hypercube graph $Q_n$ and note that finding the $k$-liminal burning number of $Q_n$ is strongly related to finding an appropriate Sperner family—a family of sets where no element is a proper subset of another. We introduce a variant of these Sperner families that, alongside other methods, allows us to establish bounds on $b_k(Q_n)$ for various values of $k$. We also determine the exact cooling number of the $n$-dimensional hypercube to be $n.$
Joint work with: Anthony Bonato, Trent Marbach, John Marcoux
Zoom link:

Details

Date:
October 22, 2025
Time:
3:30 pm - 4:30 pm
Event Category:

Venue

Online via Zoom

Organizer

jeannette Janssen
Phone:
(902) 494-8851
Email:
jeannette.janssen@dal.ca
Website:
https://www.dal.ca/faculty/science/math-stats/faculty-staff/our-faculty/mathematics/jeannette-janssen.html