University of Victoria

An (m,n)-mixed graph consists of colored edges and colored arcs. MacGillivray and Trey extended Moon’s idea of a k-universal target graph to (m,n)-mixed graphs. In particular, they constructed an (m,n)-mixed graph H such that every (m,n)-mixed graph...

Given two $n \times n$ latin squares $L$ and $M$, define their intersection size as the number of common entries when the squares are overlayed: $|\{(i,j) \in [n]^2:L_{ij}=M_{ij}\}|$. The set of all possible intersection sizes between two $n \times n...

In 1964, JW Moon constructed a k-universal graph, for every fixed integer k. This is a (large) graph that contains every graph on k vertices as an induced subgraph. In 1968, he used a similar method to construct, for every fixed integer k, a k...

Enumerating matroid extensions is a surprisingly difficult problem. One strategy is to relate extensions of certain matroids to stable sets in an auxiliary graph and use methods, like the container method, to count stable sets. In this talk, I will...

A 1935 problem of Erdos and Szekeres asks for the smallest number, r(n), such that given any collection of r(n) points in the plane there exist n points no 3 of which are the vertices of a right triangle. It is known that r(4) = 8, 9, or 10, and in...

The game of Cops and Robbers is a two-player pursuit–evasion game played on a graph, in which a set of cops attempts to capture a single robber. In the original version, players occupy vertices and take turns moving along edges. We describe a variant...

The classic Lotka-Volterra model for species competition has traditionally been associated with ecological settings where living species compete for limited resources. Here I will discuss two recent examples from work in my group where similar ideas...

A Latin square of order $n$ is an $n\times n$ grid of $n$ symbols each appearing exactly once in every row and column. If we decompose Latin squares by symbol, we can express them as sums of permutation matrices equalling a constant matrix. In this...

Program Download the full program [pdf] for abstracts and other details. Special Guest Lecture: First Nation Leadership in Clean Energy and Climate Action Speaker: Judith Sayers, indigenous leader, Chancellor of Vancouver Island University, President...

Juvan, Malnič and Mohar [J. Combin. Theory Ser. B 68 (1996), 7-22] proved that for every surface S and every integer k, there exists N(S,k) such that any set of simple closed curves on the surface S, where any two are non-homotopic and intersect at...