Conjunctive queries select and are expected to return certain tuples from a relational
database. We study the potentially easier problem of counting all selected tuples, rather than …

Many graph parameters can be expressed as homomorphism counts to fixed target graphs;
this includes the number of independent sets and the number of k-colorings for any fixed k …

The classical Andr\'{a} sfai-Erd\H {o} sS\'{o} s Theorem states that for $\ell\ge 2$, every $ n $-
vertex $ K_ {\ell+ 1} $-free graph with minimum degree greater than $\frac {3\ell-4}{3\ell-1} n …

The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether
there exists a surjective assignment to a set of variables subject to some specified …

We study the problem of counting the number of homomorphisms from an input graph $ G $
to a fixed (quantum) graph $\bar {H} $ in any finite field of prime order $\mathbb {Z} _p $. The …

Learning on graphs, particularly graph classification, requires rich graph representations. A
common paradigm to obtain these is by extracting sets of substructures and representing …

This thesis investigates fundamental problems in approximate counting that arise in the field
of statistical mechanics. Building upon recent advancements in the area, our research aims …

Let G be a graph that contains an induced subgraph H. A retraction from G to H is a
homomorphism from G to H that is the identity function on H. Retractions are very well …

Many natural combinatorial quantities can be expressed by counting the number of
homomorphisms to a fixed relational structure. For example, the number of 3-colorings of an …

Focke, Goldberg, and\v {Z} ivn\'y (arXiv 2017) prove a complexity dichotomy for the problem
of counting surjective homomorphisms from a large input graph G without loops to a fixed …