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Atlantic Graph Theory Seminar: Caleb Jones and Rylo Ashmore (Memorial University)
March 15, 2023 @ 3:30 pm - 4:30 pm
Speaker 1: Caleb Jones, Memorial University
Title: Extending Graph Burning to Hypergraphs
We introduce a round-based model much like graph burning which applies to hypergraphs. The rules for this new model are very natural,and generalize the original model of graph burning. We also introduce a variant called lazy hypergraph burning, along with a new parameter, the lazy burning number. Interestingly, lazily burning a graph is trivial, while lazily burning a hypergraph can be quite complicated. Moreover, the lazy burning model is a useful tool for analyzing the round-based model on hypergraphs. We obtain bounds on the burning number and lazy burning number of a hypergraph in terms of its parameters.
Speaker 2: Rylo Ashmore, Memorial University
Title: Herding Cats Stuck in Trees.
In the game of Cat Herding on a graph, one player (the herder) will omnipresently delete edges, while the other player (the cat) is on a vertex of the graph, and will move along any path to a new vertex. Eventually, the cat is isolated on a single vertex, and the cat’s objective is to delay this event, while the herder tries to hasten it. In an optimally played game, the number of cuts the herder made to isolate the cat is the cat number of the graph. In this talk, we will investigate this graph parameter for both dense and sparse graphs. We will see an argument that the asymptotic behaviour of the cat number of complete graphs is n^2/3. We also look at an unexpected connection between cat herding on trees and Fibonacci numbers. In particular, we will see that trees with maximum cat number amongst graphs with n vertices have cat number asymptotically log_φ (n).
Zoom link: https://us02web.zoom.us/j/86415230827?pwd=QUxLUnlMdWYzL05zSUJ4bnBCOUJnZz09
Meeting ID: 864 1523 0827