Related papers: Fine-grained complexity of the list homomorphism p…

For graphs $G$ and $H$, an $H$-coloring of $G$ is an edge-preserving mapping from $V(G)$ to $V(H)$. In the $H$-Coloring problem the graph $H$ is fixed and we ask whether an instance graph $G$ admits an $H$-coloring. A generalization of this…

A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of…

In this paper, we study the parallel and the space complexity of the graph isomorphism problem (\GI{}) for several parameterizations. Let $\mathcal{H}=\{H_1,H_2,\cdots,H_l\}$ be a finite set of graphs where $|V(H_i)|\leq d$ for all $i$ and…

For a graph $H$, a graph $G$ is an $H$-graph if it is an intersection graph of connected subgraphs of some subdivision of $H$. $H$-graphs naturally generalize several important graph classes like interval or circular-arc graph. This class…

We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…

We consider the problem of finding a homomorphism from an input digraph $G$ to a fixed digraph $H$. We show that if $H$ admits a weak near unanimity polymorphism $\phi$ then deciding whether $G$ admits a homomorphism to $H$ (HOM($H$)) is…

For digraphs $D$ and $H$, a mapping $f: V(D)\dom V(H)$ is a homomorphism of $D$ to $H$ if $uv\in A(D)$ implies $f(u)f(v)\in A(H).$ For a fixed digraph $H$, the homomorphism problem is to decide whether an input digraph $D$ admits a…

A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…

Many problems in extremal graph theory correspond to questions involving homomorphisms into a fixed image graph. Recently, there has been interest in maximizing the number of homomorphisms from graphs with a fixed number of vertices and…

Given a graph $G$ and a target graph $H$, an $H$-coloring of $G$ is an adjacency-preserving vertex map from $G$ to $H$. The number of $H$-colorings of $G$, $\hom(G,H)$, has been studied for many classes of $G$ and $H$. In particular,…

For digraphs $G$ and $H$, a homomorphism of $G$ to $H$ is a mapping $f:\ V(G)\dom V(H)$ such that $uv\in A(G)$ implies $f(u)f(v)\in A(H)$. If, moreover, each vertex $u \in V(G)$ is associated with costs $c_i(u), i \in V(H)$, then the cost…

A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices of H that preserves edges. A homomorphism is surjective if it uses all of the vertices of H and it is a compaction if it uses all of the…

We study the problem of computing the parity of the number of homomorphisms from an input graph $G$ to a fixed graph $H$. Faben and Jerrum [ToC'15] introduced an explicit criterion on the graph $H$ and conjectured that, if satisfied, the…

Given a loop-free graph $H$, the reconfiguration problem for homomorphisms to $H$ (also called $H$-colourings) asks: given two $H$-colourings $f$ of $g$ of a graph $G$, is it possible to transform $f$ into $g$ by a sequence of single-vertex…

Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…

Let $H$ be a fixed graph on $n$ vertices. Let $f_H(G) = 1$ iff the input graph $G$ on $n$ vertices contains $H$ as a (not necessarily induced) subgraph. Let $\alpha_H$ denote the cardinality of a maximum independent set of $H$. In this…

Counting problems in general and counting graph homomorphisms in particular have numerous applications in combinatorics, computer science, statistical physics, and elsewhere. One of the most well studied problems in this area is…

We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable,…

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 subproblem with graph $H$ was introduced by Faben and Jerrum…

We introduce the tree distance, a new distance measure on graphs. The tree distance can be computed in polynomial time with standard methods from convex optimization. It is based on the notion of fractional isomorphism, a characterization…