Many fundamental theorems in extremal graph theory can be expressed as algebraic inequalities between subgraph densities. As is explained below, for dense graphs, it is possible to replace subgraph densities with homomorphism densities. An easy observation shows that one can convert any algebraic inequality between homomorphism densities to a linear inequality. Inspired by the work of Freedman,...

Partee (1986) claimed without proof that the function BE is the only homomorphism that makes the Partee triangle commute. This paper shows that this claim is incorrect unless “homomorphism” is understood as “complete homomorphism.” It also shows that BE and A are the inverses of each other on certain natural assumptions.

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 ...

This paper exhibits a Monte Carlo study on site percolation using the Newmann-Ziff algorithm in distorted square and simple cubic lattices where each is allowed to be directly linked with any other if Euclidean separation between pair at most certain distance $d$, called connection threshold. Distorted are formed from regular by random but controlled dislocation of sites help parameter $\ensure...

ρ(e)(x) = e · x A1 = x = 1X(x) for all g, h ∈ G and x ∈ X. Thus ρ(gh) = ρ(g) ◦ ρ(h), ρ(e) = 1X and ρ is hence a homomorphism of monoids G → M(X). Then we note 1X = ρ(e) = ρ(gg ) = ρ(g) ◦ ρ(g) and similarly 1X = ρ(g) ◦ ρ(g) and so the ρ(g) are bijections G → G for all g ∈ G. Thus ρ is a homomorphism G → Σ(X). Given a homomorphism λ : G → Σ(X), in order for it to be the action homomorphism of an ...

We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propo...

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). If, moreover, each vertex u ∈ V (D) is associated with costs ci(u), i ∈ V (H), then the cost of the homomorphism f is ∑ u∈V (D) cf(u)(u). For each fixed digraph H, we have the minimum cost homomorphism problem for H. The problem is to decide, for an input graph D with costs ci(u), u...

By establishing a connection between the sigma polynomial and the homomorphism polynomial, many of the proofs for computing the sigma polynmial are simplified, the homomorphism polynomial can be identified for several new classes of graphs, and progress can be made on identifying homomorphism polynomials.

Let K and L be lattices, and let φ be a homomorphism of K into L. Then φ induces a natural 0-preserving join-homomorphism of ConK into ConL. Extending a result of A. Huhn, the authors proved that if D and E are finite distributive lattices and ψ is a 0-preserving join-homomorphism from D into E, then D and E can be represented as the congruence lattices of the finite lattices K and L, respectiv...