For digraphs G and H , a homomorphism of G to H is a mapping f : V (G)→V (H) such that uv ∈ A(G) implies f(u)f(v) ∈ A(H). In the minimum cost homomorphism problem we associate costs ci(u), u ∈ V (G), i ∈ V (H) with the mapping of u to i and the cost of a homomorphism f is defined ∑ u∈V (G) cf(u)(u) accordingly. Here the minimum cost homomorphism problem for a fixed digraph H , denoted by MinHOM...

With a graph G = (V,E) we associate a collection of non-negative real weights ⋃ v∈V {λi,v : 1 ≤ i ≤ m} ∪ ⋃ uv∈E{λij,uv : 1 ≤ i ≤ j ≤ m}. We consider the probability distribution on {f : V → {1, . . . ,m}} in which each f occurs with probability proportional to ∏ v∈V λf(v),v ∏ uv∈E λf(u)f(v),uv . Many well-known statistical physics models, including the Ising model with an external field and the...

We compute a twisted first cohomology group of the automorphism group of a free group with coefficients in the abelianization V of the IA-automorphism group of a free group. In particular, we show that it is generated by two crossed homomorphisms constructed with the Magnus representation and the Magnus expansion due to Morita and Kawazumi respectively. As a corollary, we see that the first Joh...

In 2004, Berdine, Calcagno and O’Hearn introduced a fragment of separation logic that allows for reasoning about programs with pointers and linked lists. They showed that entailment in this fragment is in coNP, but the precise complexity of this problem has been open since. In this paper, we show that the problem can actually be solved in polynomial time. To this end, we represent separation lo...

Graph homomorphism is an ubiquitous notion in graph theory with a variety of applications, and a first step to understanding more general constraints given by relational structures, see e.g. the monograph of Hell and Nešetřil [5]. We write μ : G→ H if μ is a homomorphism from the graph G to H, or simply G → H if such a homomorphism exists. For example, a graph G is k-colorable iff it has a homo...

For digraphs D and H , a mapping f : V (D) → V (H) is a homomorphism of D to H if uv ∈ A(D) implies f (u)f (v) ∈ A(H). For a fixed digraph H , the homomorphism problem is to decide whether an input digraph D admits a homomorphism to H or not, and is denoted as HOM(H). An optimization version of the homomorphism problemwasmotivated by a real-world problem in defence logistics and was introduced ...

For any abelian Polish σ-compact group H there exist an Fσ ideal Z ⊆ P (N) and a Borel Z -approximate homomorphism f : H → HN which is not Z -approximable by a continuous true homomorphism g : H → HN .

Let H be a fixed graph without loops. We prove that if H is a co-circular arc bigraph then the minimum cost homomorphism problem to H admits a polynomial time constant ratio approximation algorithm; otherwise the minimum cost homomorphism problem to H is known to be not approximable. This solves a problem posed in an earlier paper. For the purposes of the approximation, we provide a new charact...

We consider a database composed of a set of conceptual graphs. Using conceptual graphs and graph homomorphism it is possible to build a basic query-answering mechanism based on semantic search. Graph homomorphism defines a partial order over conceptual graphs. Since graph homomorphism checking is an NP-Complete problem, the main requirement for database organizing and managing algorithms is to ...

Constraint satisfaction problems form a very interesting and much studied class of decision problems. Feder and Vardi realized their relation to general coloring problems of relational structure. This enabled the use of algebraic, combinatorial, and model theoretic methods for studying the complexity of such decision problems. In this paper we are interested in constraint satisfaction problems ...