Plenary speakers

Aida Abiad Monge
On eigenvalue bounds for the independence and chromatic number of graph powers and its applications

Spectral graph theory looks at the connection between the eigenvalues of a matrix associated with a graph and the corresponding structures of a graph.  In this talk we will show how spectral methods provide a handy tool for obtaining results concerning the structure of graphs.

In particular, we will derive eigenvalue bounds on several NP-hard distance-type graph parameters such as the independence number and the distance chromatic number of graph powers (where the k-th graph power is a graph which has the same vertex set as the original graph G, with two vertices adjacent if and only if they are at distance at most k in G).

We will then see how to use polynomials and mixed integer linear programming in order to optimize such bounds. Some infinite families of graphs for which the new bounds are tight will be shown. Finally,  some applications to other fields like coding theory will be discussed.

Dion Gijswijt
Turán numbers of affine geometries slides 

For a fixed graph H, the Turán number ex(n,H) is the maximum number of edges of an n-vertex graph G without H as a subgraph. If H is nonbipartite, the Erdős-Stone-Simonovits theorem states that ex(H,n) is roughly a constant times n2, where the constant is a function of the chromatic number of H. If H is bipartite, the situation is markedly different. The Turán number ex(H,n) is only O(n2c) for a constant c<1, and few exact asymptotics are known.

In this lecture, we consider the analogous question for subsets of a finite vector space Fqn that do not contain a fixed configuration H. There is a geometric Erdős-Stone-Simonovits theorem that gives the right asymptotics for projective configurations with critical number χ≥3. The case χ=2 (affine configurations) is again much less well-understood and will be the focus of the talk.

We will use the Croot-Lev-Pach lemma to show that for a large class of affine configurations the Turán number ex(H,n) is of the form O(qnc) for some c<1 (analogous to the case of bipartite graphs.) A prominent example is the famous Cap Set Problem, which corresponds to the configuration consisting of three points on a line. It is an open problem whether it is true for all affine configurations.

Jan van den Heuvel
Two times Erdős-Ko-Rado; or bipartite subgraphs in Kneser graphs

Intersecting set systems have been, and still are, one of the most-studied type of set systems. A family of sets is intersecting if any two of them have a non-empty intersection. If this family is formed by some k-element subsets from an n-element groundset, then the famous Erdős-Ko-Rado theorem gives an upper bound on the size of such a family.

Another way to interpret this result (and similar ones) is by using Kneser graphs. The Kneser graph Kn(n,k) has as vertex set all k-subsets of an n-set, and two vertices are joined by an edge if they are disjoint. Looking at it this way, the Erdős-Ko-Rado theorem gives an upper bound on the size of the largest independent set in a Kneser graph.

Suppose that instead of just one intersecting family of k-subsets from an n-set, we want to know how large the union of two intersecting families can be. This corresponds to looking for the largest induced bipartite subgraph in the Kneser graph Kn(n,k).

Surprisingly, we don't know in all cases what such a subgraph looks like. In the talk I give an idea of what is known, and discuss some new results (and conjectures).

This is joined work with Xinyi Xu.

Raffaella Mulas
Laplacians and colors for graphs and hypergraphs

In the first part of the talk we will discuss some properties of the normalized Laplacian for graphs and hypergraphs, as well as an application to networks of genetic expression. We will then talk about the non-backtracking Laplacian for graphs, and we will discuss some connections between Laplacians and coloring numbers.

Lightning talks

Wednesday

Adrian Rettich -- Measurable Domination on Uncountable Graphs slides 

Hannah van Santvliet -- Hall's Theorem and why combinatorics is relevant to the SAT problem slides 

Jan Bok -- Resolving Sets in Temporal Graphs slides 

Karla Leipold -- Computing the EHZ capacity is NP-Hard slides 

Khallil Berrekkal -- Weak Spatial Mixing For The Potts Model on The d-ary Tree

Lander Verlinde -- Exploration of the Ball-Serra Bound for Grid Coverings slides 

Lies Beers -- At the end of the spectrum slides 

Linpeng Zhang -- Connected Turan number of path in hypergraph slides 

Mikhail Hlushchanka -- Regularisation of bipartite graphs slides 

Otto Sumray -- Quiver Laplacians and their Spectra slides 

Paul Bastide --Distance reconstruction slides 

Sjanne Zeijlemaker -- A unified framework for the Expander Mixing Lemma for irregular graphs and its applications slides 

Thursday

Alexandros Leivaditis -- Branchwidth is (1,g)-self-dual slides 

Bas van der Beek -- Interplanetary cartography: The Earth-Moon problem slides 

David Mikšaník -- Borodin-Kostochka conjecture and related problems slides 

Helena Petri -- Roman domination and subtrees slides 

Krisztina Szilágyi -- XNLP-hardness of Parameterized Problems on Planar Graphs slides 

Michelle Sweering -- Colouring squares of random graphs slides 

Mike de Vries -- Lily pad numbers slides 

Nikola Jedličková -- On the Structure of Hamiltonian Graphs with Small Independence Number slides 

Robin Simoens -- The zero forcing number of Hamming graphs slides 

Sam Adriaensen -- Points below a parabola in affine planes of prime order slides 

Thijs van Veluw -- Hoffman colorings slides 

Yanna Kraakman -- Sampling random directed hypergraphs slides