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, and a vertex r where the fire starts at, called root. At each time step, the firefighters can protect up to B vertices of the graph while the fire spreads from burning vertices to all their neighbors that have not…

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 online algorithm which has partial control over which random edges are added. Through intelligent decision-making, the objective of the algorithm is to force the graph to satisfy a fixed graph property with high probability in as few rounds as possible. We first…

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 flows in graphs. In particular, flow-colouring duality of graphs in the plane can be re-interpreted using signed graphs in the projective plane. Also, where a flow in a graph can be viewed as a sum of flows on cycles, in…

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 of dominating sets of each cardinality in G, and its coefficients have been conjectured to be unimodal. In this talk we will show the domination polynomial of a tree T is unimodal so long as the sizes of the minimal…

Two short talks by grad students Alex Clow and William Kellough. 'Live' viewing in Chase 227 for those at Dalhousie. Talk 1: Alex Clow, Simon Fraser University Polynomially Bounding the Oriented Chromatic Number in Euler Genus In this talk we consider the oriented chromatic number of graphs with bounded Euler genus. In particular, we present our proofs that the oriented chromatic number is at most $g^{6400}$ for sufficiently large $g$ and at least $\Omega((\frac{g^2}{\log g})^{1/3})$. This is a major improvement…

Detecting (Di)Graphical Regular Representations Speaker: Joy Morris, U. Lethbridge Abstract: Graphical and Digraphical Regular Representations (GRRs and DRRs) are a concrete way to visualise the regular action of a group, using (di)graphs. More precisely, a GRR or DRR on the group $G$ is a (di)graph whose automorphism group is isomorphic to the regular action of $G$ on itself by right-multiplication. For a (di)graph to be a DRR or GRR on $G$, it must be a Cayley (di)graph on $G$. Whenever…

Speaker:  Santiago Guzman-Pro, TU Dresden Title:          Forbidden Tournaments and the Orientation (Completion) Problem Abstract:   For a fixed finite set of  oriented graphs F,  the F-free  orientation problem asks whether a given finite undirected graph G has an F-free orientation, i.e., whether the edges of  G  can be  oriented so that the  resulting  oriented  graph does not contain  any oriented graph from F as an oriented (induced) subgraph. It was first noted by Bang-Jensen, Huang, and Prisner that when F…

Speaker: Jordan Barrett, Toronto Metropolitan University Title: Graph burning, the burning number conjecture, and burning density Abstract: Graph burning is a discrete time process on a graph that acts as a simple model for the spread of social contagion in a network. Graph burning was introduced by Bonato, Janssen and Roshanbin in 2014, and with this introduction came the now famous "burning number conjecture". In the first half of my talk, I will introduce graph burning and give a brief overview of…