We study homomorphisms between randomly directed paths and give estimates on the probability of the existence of such homomorphism. We show that a random path is a core with positive probability. We apply our results in the investigation of homomorphism dualities, the most natural situation when a homomorphism (or Constraint Satisfaction) problem is in coNP.

Given two graphs G = (VG, EG) and H = (VH , EH), a homomorphism from G to H is a function f : VG → VH such that for every uv ∈ EG, f(u)f(v) ∈ EH . A homomorphism from G to H is referred to as an H-colouring of G and the vertices of H are regarded as colours. The graph H is called the target of the homomorphism. These definitions extend to directed graphs by requiring that the mapping must prese...

Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation such as a paraconsistent one (no paradox arises if the liar is both true and false). We consider a non-Fregean logic which is a revised an...

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.

We answer two open questions posed by Cameron and Nesetril concerning homomorphismhomogeneous graphs. In particular we show, by giving a characterization of these graphs, that extendability to monomorphism or to homomorphism leads to the same class of graphs when defining homomorphism-homogeneity. Further we show that there are homomorphism-homogeneous graphs that do not contain the Rado graph ...

Let G and G' be multiplicative systems. A half-homomorphism of G into G' will mean a mapping a—>a' of G into C such that for all a, bEG, (ab)'=a'V or b'a'. An anti-homomorphism is a mapping such that always (ab)' = b'a'. The terms half-isomorphism, etc., are defined similarly. It will be shown that any half-homomorphism of a group G into a group G' is either a homomorphism or an anti-homomorphi...

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...

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.