In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.

This paper continues the investigation of the rst author begun in part one. The hereditary properties of n-homomorphism amenability for Banach algebras are investigated and the relations between n-homomorphism amenability of a Banach algebra and its ideals are found. Analogous to the character amenability, it is shown that the tensor product of two unital Banach algebras is n-homomorphism amena...

A strong oriented k-coloring of an oriented graph G is a homomorphism φ from G to H having k vertices labelled by the k elements of an abelian additive group M , such that for any pairs of arcs −→ uv and −→ zt of G, we have φ(v)−φ(u) 6= −(φ(t)−φ(z)). The strong oriented chromatic number χs(G) is the smallest k such that G admits a strong oriented k-coloring. In this paper, we consider the follo...

Recall that a continuous function $fcolon Xto Y$ between Tychonoff spaces is proper if and only if the Stone extension $f^{beta}colon beta Xtobeta Y$ takes remainder to remainder, in the sense that $f^{beta}[beta X-X]subseteq beta Y-Y$. We introduce the notion of ``taking remainder to remainder" to frames, and, using it, we define a frame homomorphism $hcolon Lto M$ to be $beta$-proper, $lambd...

In this talk we will discuss some examples of graph homomorphisms. More precisely, the graph parameters which can be represented by counting the graph homomorphisms. The main reference is Section 2 in [2].

For a graph G, let     max : is an edge cut of b G D D G  . For graphs G and H, a map     :V G V H   is a graph homomorphism if for each   e uv E G   ,       u v E H    . In 1979, Erdös proved by probabilistic methods that for p ≥ 2 with

A graph homomorphism is a vertex map which carries edges from a source graph to edgesin a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem(MAX H -COL) are edge-weighted graphs G and the objective is to find a subgraph of G that hasmaximal total edge weight, under the condition that the subgraph has a homomorphism to H ;note that for H = Kk th...

Following the last talk on graph homomorphisms, we continue to discuss some examples of graph homomorphisms. But this time we will focus on some models, that is, the homomorphism G → H for the graph H with fixed weights. The main reference is Section 1 in [2].