A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.

We investigate several variants of the homomorphism problem: given two relational structures, is there a homomorphism from one to the other? The input structures are possibly infinite, but definable by first-order interpretations in a fixed structure. Their signatures can be either finite or infinite but definable. The homomorphisms can be either arbitrary, or definable with parameters, or defi...

Let A and B be Banach algebras with bounded approximate identities let Φ:A→B a surjective continuous linear map which preserves two-sided zero products (i.e., Φ(a)Φ(b)=Φ(b)Φ(a)=0 whenever ab=ba=0). We show that Φ is weighted Jordan homomorphism provided product determined weakly amenable. These conditions are in particular fulfilled when the group algebra L1(G) G any locally compact group. also...

A 2-edge-colored graph or a signed is simple with two types of edges. homomorphism from G to H mapping φ:V(G)→V(H) that maps every edge in an the same type H. Switching vertex v corresponds changing each incident v. There if after switching some subset vertices there The chromatic number (resp. signed) order smallest such class graphs maximum numbers class. We study and (connected not necessari...

We give a notion of measure on P that overcomes some limitations of earlier formulations. In the process, we investigate the significance for resource-bounded measure of the choice of the lexicographic ordering of the words. Disciplines Theory and Algorithms This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/cs_techreports/169 Measure on P: Strength...

Weconsider the colouring (or homomorphism) orderC induced by all finite graphs and the existence of a homomorphism between them. This ordering may be seen as a lattice which is far from being complete. In this paper we study bounds and suprema and maximal elements in C of some frequently studied classes of graphs (such as bounded degree, degenerated and classes determined by a finite set of for...

208 NOTICES OF THE AMS VOLUME 51, NUMBER 2 As far as I know, the notion of a quasi-morphism does not have much to do with category theory. This very natural idea underlies several interesting recent developments at the crossroads of algebra, topology, geometry, and dynamics. Other, perhaps better, names currently in use for the same concept are quasi-homomorphism and pseudo-character. Let G be ...

A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of testing whether a given graph G allows a homomorphism to a given graph H that is locally bijective, surjective, or injective, respectively, are NP-complete, even w...

A signed graph (G,?) is a G along with function ?:E(G)?{+,?}. closed walk of positive (resp., negative) if it has an even odd) number negative edges, counting repetitions. homomorphism (simple) to another vertex-mapping that preserves adjacencies and signs walks. The chromatic the minimum vertices |V(H)| (H,?) which admits homomorphism. Homomorphisms graphs have been attracting growing attentio...

the purpose of this paper is to introduce the concept of l-fuzzybilinear operators. we obtain a decomposition theorem for l-fuzzy bilinearoperators and then prove that a l-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by s.e.rodabaugh (1991).finally we discuss the continuity of l-fuzzy bilinear operators.