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.…

Speaker: Shahriyar Pourakbar Saffar, Memorial University of Newfoundland Title: Existence of uniquely 2-colourable 4-cycle decompositions: A constructive proof Abstract: A cycle system of order $n$ is a decomposition of the edges of the complete graph $K_n$ into cycles of a fixed length. A cycle system is said to be $k$-colourable if we can assign $k$ colours to its vertices so that no cycle is monochromatic. If a cycle system is $k$-colourable but not $(k-1)$-colourable, it is called $k$-chromatic. A $k$-colourable…

Speaker: Jorik Jooken, KU Leuven Kulak Title: On vertex-girth-regular graphs: (Non-)existence, bounds and enumeration Abstract: A vertex-girth-regular vgr(v,k,g,lambda)-graph is a k-regular graph of girth g and order v in which every vertex belongs to exactly lambda cycles of length g. While all vertex-transitive graphs are necessarily vertex-girth-regular, the majority of vertex-girth-regular graphs are not vertex-transitive. Similarly, while many of the smallest k-regular graphs of girth g, the so-called (k,g)-cages, are vertex-girth-regular, infinitely many vertex-girth-regular graphs of degree k and girth…

Date and Time: Wednesday, February 11, 3.40 pm Atlantic time Speaker: JD Nir, Oakland University Title: The Second Common Neighbourhood Conjecture Abstract: The Second Common Neighbourhood Conjecture is a question about the structure of shared neighbours in a graph. At first glance, it seems like a nice problem for a new researcher to study: it requires only a basic understanding of graph theory to state, examples are easy to understand, and one can quickly prove the conjecture holds in certain…

Speaker: Andrea Burgess, University of New Brunswick Title: Colourings of combinatorial designs Abstract: A combinatorial design is a pair $(V,\mathcal{B})$ where $V$ is a nonempty set of points, and $\mathcal{B}$ is a collection of subsets of $\mathcal{B}$, called blocks.  A $c$-colouring of a design $(V,\mathcal{B})$ is a function $f:V \rightarrow C$, where $C$ is a set of $c$ colours, such that each block contains at least two points of different colours.  The design's chromatic number is the least value of…