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.

The relation between the cover (Tukey type) uniformities and the entourage (Weil type) ones, in the point-free context, is studied and a transparent translation is presented. In particular the natural uniformities on localic groups are discussed, and the uniformity of localic group homomorphisms is proved.

On the space of homomorphisms from a Verma module to an indecomposable tilting module of the BGG-category O we define a natural filtration following Andersen [And97] and establish a formula expressing the dimensions of the filtration steps in terms of coefficients of Kazhdan-Lusztig polynomials.

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.

We define a class of algebraic structures for the interpretation of tabular notations common in software requirements documentation and show how to use table algebra homomorphisms to define staged table semantics, translation between different kinds of tables, and table transformation. An important advantage of this approach is that it covers the practically important use of nested headers in a...

Based on original work in [TV03], this paper gives a representation theorem for the Scott continuous maps between frames in terms of natural transformations between functors indexed by frames. The result specializes to frame homomorphisms, thereby giving a representation theorem for all locale maps (i.e. continuous maps as defined in locale theory).

It is known that the powers m of the maximal ideal of a local Noetherian ring share certain homological properties for all sufficiently large integers n. For example, the natural homomorphisms R → R/m are Golod, respectively, small, for all large n. We give effective bounds on the smallest integers n for which such properties begin to hold.

Twisted homomorphisms of bialgebras are bialgebra homomorphisms from the first into Drinfeld twistings of the second. They possess a composition operation extending composition of bialgebra homomorphisms. Gauge transformations of twists, compatible with adjacent homomorphisms, give rise to gauge transformation of twisted homomorphisms, which behave nicely with respect to compositions. Here we s...

We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some connectome graphs are described.