The 2-burning number of a graph Speaker: Ann Trenk, Wellesley College Abstract: We discuss a discrete-time model for the spread of information in a graph, motivated by the idea that people believe a story when they learn of it from two different origins. Similar to the burning number, in this problem, information spreads in rounds and a new source can appear in each round. For a graph $G$, we are interested in $b_2(G)$, the minimum number of rounds until the…

The Burning Number of Large Caterpillars Danielle Cox, Mount Saint Vincent University Abstract: In this talk we will look at the history of the graph burning conjecture and the state of the art. We will also prove the conjecture for sufficiently large p-caterpillars. This is joint work with Kerry Ojakian (CUNY) and Margaret-Ellen Messinger (Mt Allison). Zoom link: https://us02web.zoom.us/j/86861499971?pwd=rTDAaju0TCu24asnaBGvkuNlT11KZ1.1 Meeting ID: 868 6149 9971 Passcode: 325258

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…

Date and Time: Wednesday, October 29, 3.40 pm Atlantic time Speaker: Ben Moore, University of Manitoba Title: Smoothed analysis for graph isomorphism Abstract: I'll describe a simple algorithm which shows the following: Given any graph G, add or remove edges uniformly at random with probability 100/v(G) to create a graph G'. We can test in polynomial time if G' is isomorphic to any other graph H. In other words, graph isomorphism is in P if you add a little bit of randomness to the…

Date and Time: Wednesday, November 5, 3.40 pm Atlantic time Speaker: Kalina Petrova, Institute of Science and Technology Austria Title: Cameron's conjecture on random Latin squares Abstract: A conjecture of Cameron states that the distribution of the number of odd rows in an n x n uniformly random Latin square is approximately binomial with n trials and success probability 1/2. We prove this conjecture in several different senses, including total variation convergence, a local central limit theorem, and a large deviation principle. In fact,…

Date and Time: Wednesday, November 19, 3.40 pm Atlantic time Speaker: Rachel Kirsch, George Mason University Title: Maximizing subgraph density by double counting Abstract: This talk will highlight the use of the method of counting in two ways in recent research on maximizing subgraph density in graphs of bounded degree and clique number. Zoom link: https://us02web.zoom.us/j/88013261876?pwd=XGocyHqvseXY8metPztPoSuulEEejX.1 Meeting ID: 880 1326 1876 Passcode: 357963

Date and Time: Wednesday, November 26, 3.40 pm Atlantic time Speaker: Himanshu Gupta, University of Regina Title: On the eigenvalues of the graphs D(5, q) Abstract: In 1995, Lazebnik and Ustimenko introduced the family of q-regular graphs D(k, q), which is defined for any positive integer k and prime power q. The connected components of the graph D(k, q) have provided the bestknown general lower bound on the size of a graph for any given order and girth to this…

Colourings of Balanced Incomplete Block Designs That Are Almost Locally Equitable Date and Time: Wednesday, January 14, 3.40 pm Atlantic time Speaker: William Kellough, Memorial University of Newfoundland Abstract: In this talk, we study $\ell$-colourings of $(v,k,\lambda)$-BIBDs where within each block, one colour is absent and the rest appear exactly $\frac{k}{\ell-1}$ times. We give necessary conditions for such colourings to exist. We show how Hadamard matrices, affine planes, and twin prime powers can be used to construct such coloured BIBDs.…