Let be a graph on and a positive integer. Let be the abstract simplicial complex whose faces are the subsets of that do not contain an independent set of size in . We study the collapsibility numbers of for various classes of graphs, focusing on the class of …
For any given graph , one may define a natural corresponding functional for real-valued functions by using homomorphism density. One may also extend this to complex-valued functions, once is paired with a -edge-colouring to assign conjugates. We say that is real-norming (resp. complex-norming) if (resp. there is such that …
The asymptotic dimension of metric spaces is an important notion in geometric group theory. The metric spaces considered in this talk are the ones whose underlying spaces are the vertex-sets of (edge-)weighted graphs and whose metrics are the distance functions in weighted graphs. A standard compactness argument shows that it suffices to consider the asymptotic …
We introduce some of well-known game-theoretic graph models and related problems. A contagion game model explains how an innovation diffuses over a given network structure and focuses on finding conditions on which structure an innovation becomes epidemic. Regular infinite graphs are interesting examples to explore. We show that regular infinite trees make an innovation least …
