Tuesday, Feb 15, 4pm ET (9pm GMT, 10am Wed NZDT)
Chun-Hung Liu, Texas A&M University
Homomorphism counts in robustly sparse graphs

Abstract:

For a fixed graph $H$ and for arbitrarily large host graphs $G$, the number
of homomorphisms from $H$ to $G$ and the number of subgraphs isomorphic to $H$
contained in $G$ have been extensively studied when the host graphs are
allowed to be dense. This talk addresses the case when the host graphs
are robustly sparse. We determine, up to a constant multiplicative
error, the maximum number of subgraphs isomorphic to $H$ contained in an
$n$-vertex graph in any fixed hereditary graph class with bounded
expansion. This result solves a number of open questions and can be
generalized to counting the number of homomorphisms.

Tuesday, Feb 8, 3pm ET (8pm GMT, 9am Wed NZDT)
Sophie Spirkl and James Davies, University of Waterloo
Two counterexamples related to chi-boundedness

Abstract:

Sophie Spirkl: I will present a counterexample to the following well-known conjecture: for every $k$, $r$, every graph $G$ with clique number at most $k$ and sufficiently large chromatic number contains a triangle-free induced subgraph with chromatic number at least $r$.
Joint work with Alvaro Carbonero, Patrick Hompe, and Benjamin Moore.

James Davies: We construct hereditary classes of graphs that are $\chi$-bounded but not polynomially $\chi$-bounded.
Joint work with Marcin Briański and Bartosz Walczak.

Tuesday, Feb 1, 3pm ET (8pm GMT, 9am Wed NZDT)
Matthew Coulson, University of Waterloo
Strong components of the directed configuration model

Abstract:

We study the behaviour of the largest components of the directed configuration model in the barely subcritical regime. We show that with high probability all strongly connected components in this regime are either cycles or isolated vertices and give an asymptotic distribution of the size of the kth largest cycle. This gives a configuration model analogue of a result of Luczak and Seierstad for the binomial random digraph.

Tuesday, Jan 25, 3pm ET (8pm GMT, 9am Wed NZDT)
Archontia Giannopoulou, University of Athens
A Matching Theoretic Flat Wall Theorem

Abstract:

One of the key theorems in Graph Minors is the Flat Wall Theorem which asserts the existence of a large wall under certain conditions. In this talk, we discuss about graphs with perfect matchings and their relationship with digraphs. Our main focus is on a matching theoretic analogue of the Flat Wall Theorem for bipartite graphs excluding a fixed matching minor. The tight relationship between structural digraph theory and matching theory that allows us to obtain the aforementioned version of Flat Wall Theorem further allow us to deduce a Flat Wall Theorem for digraphs which substantially differs from a previously established directed variant of this theorem.

Joint work with Sebastian Wiederrecht.