Conditions for perfect matchings in random sparse bipartite graphs Given a uniformly random sparse matrix A, with specified number of nonzero entries in columns and rows, we determine when A has full row rank over a finite field. As a

Colourings, Polynomials and Roots A lot has happened since graph colourings first arose as an applied problem in cartography – do four colours always suffice to distinguish countries when colouring a map? Along the way to the proof, the related

Progress towards the Burning Number Conjecture The burning number b(G) of a graph G is the smallest integer k such that G can be covered by k balls of radii respectively 0,...,k-1, and was introduced independently by Brandenburg and Scott at Intel as a transmission problem on processors and Bonato, Janssen

Speaker 1: Isaac McMullin Existence of Optimal Split Reliability Polynomials One of the most common models of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability p. On one hand, one

Avoiding additive powers in words A word is a sequence of symbols taken from some finite alphabet. A square is a word of the form xx, where x is a nonempty word. It is well-known that there are infinite words

Speaker 1: Caleb Jones, Memorial University   Title: Extending Graph Burning to Hypergraphs   Abstract: 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

Approximation Schemes for Resource Minimization for Fire Containment Resource Minimization Fire Containment (RMFC) is a natural model for optimal inhibition of harmful spreading phenomena on a graph. In the RMFC problem on trees, we are given an undirected tree G,

Approximation Schemes for Resource Minimization for Fire Containment The semi-random graph process is an example of an adaptive process for constructing a graph in which random edges are added step by step.  It is adaptive in that there is an

Time: 3.30pm, Atlantic time, Wednesday Sept.20 Speaker: Jessica McDonald, Auburn University Title: On flows (and group-connectivity) in signed graphs Abstract: In this talk we'll start by discussing flows in signed graphs and how it generalizes the usual notion of integer

Speaker: Iain Beaton, Acadia University Title: On the Unimodality of Nearly-Well Dominated Trees Abstract: A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination polynomial of a graph G is the generating function of the number