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November 2020

Atlantic Graph Theory Seminar: Dr Andrea Burgess (University of New Brunswick, Saint John)

November 4, 2020 @ 3:30 pm - 4:30 pm
Zoom seminar

Equitably colourable cycle decompositions A $c$-colouring of a decomposition of a graph $G$ is an assignment of $c$ colours to the vertices of $G$. A colouring is equitable if each colour is represented (as closely as possible) an equal number of times on each block, i.e. for any two colours $i$ and $j$, the number of vertices of colour $i$ and $j$ in any given block differ by at most 1. In this talk, we give an overview of colourings…

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Atlantic Graph Theory Seminar: Kyle MacKeigan (PhD Candidate, Dalhousie University)

November 18, 2020 @ 3:30 pm - 4:30 pm
Zoom seminar

Orthogonal Colourings of Graphs Two colourings of a graph are orthogonal if they have the property that when two vertices receive the same colour in one colouring, then those vertices receive distinct colours in the other colouring. In this talk, the importance of perfect orthogonal colourings is demonstrated. Then, perfect orthogonal colourings of Cayley graphs and tree graphs are constructed. To conclude, it is shown how the Cartesian, tensor, and strong graph product can be used to generate perfect orthogonal…

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Atlantic Graph Theory Seminar: Dr Jared Howell (Memorial University of Newfoundland, Grenfell Campus)

November 25, 2020 @ 3:30 pm - 4:30 pm
Zoom seminar

Gracefully labelling windmills using Skolem-like sequences To gracefully label a graph G, assign each vertex v ∊ V(G) a distinct label l(v) from {0,1,2,...,|E(G)|}, such that {|l(u)-l(v)| : uv ∊ E(G)}={1,2,3,...,|E(G)|}. In this talk we will examine constructive techniques using Skolem-like sequences to gracefully label windmills of cycles. This includes new constructive techniques for known results as well as new results on windmills with vanes of mixed cycle length. The Atlantic Graph Theory Seminar series will take place every Wednesday…

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December 2020

Atlantic Graph Theory Seminar: Dr Melissa Huggan (Ryerson University)

December 2, 2020 @ 3:30 pm - 4:30 pm
Zoom seminar

The Cheating Robot and Insider Information Throughout this talk, we explore a deterministic model as an alternative approach to studying simultaneous play combinatorial games. We call this the Cheating Robot model. This model forces both players to move at the same time, but one player has extra information about where their opponent is going to move and can react accordingly. We discuss some general theory and explore a case study to get some insight into this model. This is joint…

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Atlantic Graph Theory Seminar: Dr Erin Meger (Université du Québec à Montréal)

December 9, 2020 @ 3:30 pm - 4:30 pm
Zoom seminar

The Iterated Local Model for Social Networks Complex networks are said to exhibit four key properties: large scale, evolving over time, small world properties, and power law degree distribution. The Preferential Attachment Model (Barab´asi–Albert, 1999) and the ACL Preferential Attachment Model (Aiello, Chung, Lu, 2001) for random networks, evolve over time and rely on the structure of the graph at the previous time step. Further models of complex networks include: the Iterated Local Transitivity Model (Bonato, Hadi, Horn, Pralat, Wang,…

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January 2021

Atlantic Graph Theory Seminar: Dr Stephen Finbow, Saint Francis Xavier University

January 13, 2021 @ 3:30 pm - 4:30 pm
Zoom seminar

The γ-graph of a graph For a graph G = (V, E), the γ-graph of G, G(γ) = (V (γ), E(γ)), is the reconfiguration graph whose vertex set is the collection of minimum dominating sets, or γ-sets of G, and two γ-sets are adjacent in G(γ) if they differ by a single vertex and the two different vertices are adjacent in G. The γ-graph of G was introduced by Fricke et al. in 2011 where they studied properties of γ-graphs,…

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Atlantic Graph Theory Seminar: Dr. Hugh Thomas, UQAM

January 20, 2021 @ 3:30 pm - 4:30 pm
Zoom seminar

Dynamical algebraic combinatorics and independence sets of graphs Dynamical algebraic combinatorics is a relatively new (and fun!) topic, which looks at cyclic group actions on objects from algebraic combinatorics, inspired by some questions coming from dynamical systems. I will give an introduction to the area, focusing on an action I have defined with Nathan Williams on the independent sets of a graph (arXiv:1805.00815). We also construct a partial order on the set of independent sets of a graph, which may…

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Atlantic Graph Theory Seminar: Jordan Barrett, PhD Candidate, McGill University

January 27, 2021 @ 3:30 pm - 4:30 pm
Zoom seminar

The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

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February 2021

Atlantic Graph Theory Seminar: Dr Anthony Bonato, Ryerson University

February 10, 2021 @ 3:30 pm - 4:30 pm
Zoom seminar

The localization game played on graph Graph searching investigates combinatorial models for the detection or neutralization of an adversary’s activity on a network. One such model is the localization game, where pursuers use distance probes to capture an invisible evader. We present new results on the localization number of a graph, which is the minimum number of pursuers needed to capture the evader. We survey what is known and unknown for the localization number, discuss connections with the chromatic number,…

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Atlantic Graph Theory Seminar: Dr. Gary Gordon, Lafayette College

February 24, 2021 @ 3:30 pm - 4:30 pm
Zoom seminar

Permutations of finite subsets of R^2 generated by Euclidean distances Given a finite set of points S = {P1, P2, . . . , Pn} and a vantage point V, generate an ordering of the points of S by measuring the Euclidean distance from V to each of the points of S, ordering them from nearest to farthest. As the vantage point moves around the plane, different orderings will be generated. We are interested in the maximum, minimum, and intermediate…

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