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## October 2023

### Atlantic Graph Theory Seminar

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…

Find out more »## November 2023

### Atlantic Graph Theory Seminar

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…

Find out more »### Atlantic Graph Theory Seminar

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…

Find out more »### Atlantic Graph Theory Seminar

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…

Find out more »## January 2024

### Atlantic Graph Theory Seminar

Speaker: Leslie Hogben, Iowa State University Title: Forts, (fractional) zero forcing, and Cartesian products of graphs Abstract: Zero forcing is an iterative process that repeatedly applies a rule to change the color of vertices of a graph $G$ from white to blue. The zero forcing number is the minimum number of initially blue vertices that are needed to color all vertices blue through this process. Standard zero forcing was introduced about fifteen years ago in the control of…

Find out more »### Atlantic Graph Theory Seminar

Speaker: Torsten Mütze, Un. Warwick Title: Kneser graphs are Hamiltonian Abstract: For integers k>=1 and n>=2k+1, the Kneser graph K(n,k) has as vertices all k-element subsets of an n-element ground set, and an edge between any two disjoint sets. It has been conjectured since the 1970s that all Kneser graphs admit a Hamilton cycle, with one notable exception, namely the Petersen graph K(5,2). This problem received considerable attention in the literature, including a recent solution for the sparsest case…

Find out more »### Atlantic Graph Theory Seminar

Speaker: Thiago de Holleben, Dalhousie University Title: Homological invariants of graphs with no induced cycles of length divisible by 3 Abstract: If G is a graph with large chromatic number, what can we say about its induced subgraphs? In 2014, Bonamy et al. showed that if a graph has no induced cycles of length divisible by three, then its chromatic number is bounded. Such graphs are called ternary. In an attempt to better understand the structure of the induced subgraphs…

Find out more »## February 2024

### Atlantic Graph Theory Seminar

Zoom link below. Live viewing for local participants in Chase 227 (tea-drinkers are encouraged to bring their own mug). Speaker: Evelyn Smith-Roberge, Georgia Tech Title:Correspondence Packings of Planar Graphs Abstract: Suppose a graph G has list chromatic number k. It is easy to see that if L is a (k+1)-list assignment for G, then G admits two L-colourings f and g where f(v) =/= g(v) for every vertex v in the graph. But what if we want still more disjoint…

Find out more »### Atlantic Graph Theory Seminar

Speaker: Andrew Beveridge, Macalester College Title: Approval Ballot Triangles Time: Wednesday, February 14, 3.30pm Atlantic time Live viewing for local participants in Chase 227, Dalhousie University Bertrand's Ballot Problem enumerates the number of ways to count ballots so that candidate 1 never trails candidate 2. We generalize this problem by considering an approval ballot election between $n$ candidates. In an approval ballot election, each voter endorses a subset of candidates, rather than voting for just one person. The general approval…

Find out more »### Atlantic Graph Theory Seminar

Speaker: Ada Chan, York University Title: Polygamy in state transferAbstract:Let $X$ be a graph and $H$ be a Hermitian matrix associated with $X$. The continuous-time quantum walk with Hamiltonian $H$ isdefined by the time-dependent unitary matrix\begin{equation*}U(t)=e^{i t H}.\end{equation*}Perfect state transfer occurs from vertex $a$ to vertex $b$ at time $\tau$ is $\vert U(\tau)_{b,a}\vert = 1$. This phenomenon is relevant for information transmission in a quantum spin network. For real and symmetric Hamiltonians, it is known that perfect state transfer can…

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