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…

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…

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…

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…

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…