For every pair of nite connected graphs F and H, and every integer k, we construct a universal graph U with the following properties: 1. There is a homomorphism : U ! H, but no homomorphism from F to U . 2. For every graph G with maximal degree no more than k having a homomorphism h : G! H, but no homomorphism from F to G, there is a homomorphism : G! U , such that h = . Particularly, this solv...

The chromatic sum Σ(G) of a graph G is the smallest sum of colors among of proper coloring with the natural number. In this paper, we introduce a necessary condition for the existence of graph homomorphisms. Also, we present Σ(G) < χf (G)|G| for every graph G.

We consider the complexity of oriented homomorphism and two of its variants, namely strong oriented homomorphism and pushable homomorphism, for planar graphs with large girth. In each case, we consider the smallest target graph such that the corresponding homomorphism is NP-complete. These target graphs T4, T5, and T6 have 4, 5, and 6 vertices, respectively. For i ∈ {4, 5, 6} and for every g, w...

In this paper, we study the fundamental algorithmic problem of determining the homomorphisms from an Amodule M to an A-module N over an algebra A. We shall outline an algorithm for the case that A is a finite dimensional algebra over a finite field F and both modules M and N are finitely generated as A-modules. More specifically, the input to our algorithm consists of the following data: The mo...

The irreducible finite-dimensional representations of quantum affine algebras Uq(ĝ) have been studied from various viewpoints, [AK], [CP1], [CP3], [C], [CP4], [FR], [FM], [KR], [KS]. These representations decompose as a direct sum of irreducible representations of the quantized eneveloping algebra Uq(g) associated to the underlying finite-dimensional simple Lie algebra g. But, except for a few ...

We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather different. Our main results are partial characterisations of countable graphs and posets with this property; an analogue of Fraı̈ssé’s Theorem; and representations of monoids as endomorphism monoids of such structures. ∗This...

This paper introduces accumulation into list homomorphisms for systematic development of both efficient and correct parallel programs. New parallelizable recursive pattern called H-homomorphism is given, and transformations from sequential patterns in the H-form and Hform into (H-)homomorphism are shown. We illustrate the power of our formalization by developing a novel and general parallel pro...