相关论文: The Complexity of Approximately Counting Retractio…
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-studied: Given $H$, the complexity of deciding whether…
We examine the computational complexity of approximately counting the list H-colourings of a graph. We discover a natural graph-theoretic trichotomy based on the structure of the graph H. If H is an irreflexive bipartite graph or a…
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 HomsTo$H$ of counting, modulo 2, the homomorphisms from an input graph to a fixed undirected graph $H$. A characteristic feature of modular counting is that cancellations make wider classes of instances tractable than…
Given a graph $G$ and two graph homomorphisms $\alpha$ and $\beta$ from $G$ to a fixed graph $H$, the problem $H$-Recoloring asks whether there is a transformation from $\alpha$ to $\beta$ that changes the image of a single vertex at each…
We consider the problem of counting H-colourings from an input graph G to a target graph H. We show that if H is any fixed graph without trivial components, then the problem is as hard as the well-known problem #BIS, which is the problem of…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
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 G and H be two cographs. We show that the problem to determine whether H is a retract of G is NP-complete. We show that this problem is fixed-parameter tractable when parameterized by the size of H. When restricted to the class of…
Characterizing the graph classes such that, on $n$-vertex $m$-edge graphs in the class, we can compute the diameter faster than in ${\cal O}(nm)$ time is an important research problem both in theory and in practice. We here make a new step…
Counting homomorphisms of a constant sized pattern graph $H$ in an input graph $G$ is a fundamental computational problem. There is a rich history of studying the complexity of this problem, under various constraints on the input $G$ and…
Given graphs $H$ and $G$, possibly with vertex-colors, a homomorphism is a function $f:V(H)\to V(G)$ that preserves colors and edges. Many interesting counting problems (e.g., subgraph and induced subgraph counts) are finite linear…
We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices, so as to minimize the maximum stretch of any edge, subject to the constraint that the…
We study two computational problems, parameterised by a fixed tree H. #HomsTo(H) is the problem of counting homomorphisms from an input graph G to H. #WHomsTo(H) is the problem of counting weighted homomorphisms to H, given an input graph G…
An ordered graph is a graph enhanced with a linear order on the vertex set. An ordered graph is a core if it does not have an order-preserving homomorphism to a proper subgraph. We say that $H$ is the core of $G$ if (i) $H$ is a core, (ii)…
We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…
This paper studies the problem of counting homomorphisms from a bipartite source graph to a bipartite target graph. An exact formula is first derived for the number of homomorphisms from a complete bipartite graph into a general bipartite…
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 study the complexity of the following related computational tasks concerning a fixed countable graph G: 1. Does a countable graph H provided as input have a(n induced) subgraph isomorphic to G? 2. Given a countable graph H that has a(n…
Given a graph G, we investigate the question of determining the parity of the number of homomorphisms from G to some other fixed graph H. We conjecture that this problem exhibits a complexity dichotomy, such that all parity graph…