In the model of randomly perturbed graphs we consider union a deterministic graph $\mathcal{G}_\alpha$ with minimum degree $\alpha n$ and binomial random $\mathbb{G}(n,p)$. This was introduced by Bohman, Frieze, Martin for Hamilton cycles their result bridges gap between Dirac's theorem results Pósa Korshunov on threshold in this note extend $\mathcal{G}_\alpha\cup\mathbb{G}(n,p)$ to sparser $\...

For a given pair of maps f, g : X → M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism Λfg : H(X) → H(M) of degree (−n). We prove a Lefschetztype coincidence theorem: if the Lefschetz homomorphism is nontrivial then there is an x ∈ X such that f(x) = g(x).

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). If moreover each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of a homomorphism f is ∑ u∈V (G) cf(u)(u). For each fixed digraph H, the minimum cost homomorphism problem for H, denoted MinHOM(H), is the following problem. Given an input digraph G, ...

A knot in a solid torus defines map on the set of (smooth or topological) concordance classes knots S 3 S^3 ...

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...