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DTSTART;TZID=UTC:20251022T153000
DTEND;TZID=UTC:20251022T163000
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CREATED:20251017T111210Z
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UID:8339-1761147000-1761150600@aarms.math.ca
SUMMARY:Atlantic Graph Theory Seminar
DESCRIPTION:Date and Time: Wednesday\, October 22\, 3.40 pm Atlantic time\nSpeaker: Theodore (Teddy) Mishura\, Toronto Metropolitan University\nTitle: Liminal burning the hypercube\n \nAbstract: 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 $n.$\n\nJoint work with: Anthony Bonato\, Trent Marbach\, John Marcoux\n\nZoom link:\nhttps://us02web.zoom.us/j/88013261876?pwd=XGocyHqvseXY8metPztPoSuulEEejX.1 \nMeeting ID: 880 1326 1876\nPasscode: 357963
URL:https://aarms.math.ca/event/atlantic-graph-theory-seminar-31/
LOCATION:Online via Zoom
CATEGORIES:AARMS Atlantic Graph Theory Seminar
ORGANIZER;CN="jeannette%20Janssen":MAILTO:jeannette.janssen@dal.ca
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