2,070 research outputs found
A Study of -dipath Colourings of Oriented Graphs
We examine -colourings of oriented graphs in which, for a fixed integer , vertices joined by a directed path of length at most must be
assigned different colours. A homomorphism model that extends the ideas of
Sherk for the case is described. Dichotomy theorems for the complexity of
the problem of deciding, for fixed and , whether there exists such a
-colouring are proved.Comment: 14 page
On First-Order Definable Colorings
We address the problem of characterizing -coloring problems that are
first-order definable on a fixed class of relational structures. In this
context, we give several characterizations of a homomorphism dualities arising
in a class of structure
Rips construction without unique product
Given a finitely presented group we produce a short exact sequence such that is a torsion-free
Gromov hyperbolic group without the unique product property and is without
the unique product property and has Kazhdan's Property (T). Varying we
show a wide diversity of concrete examples of Gromov hyperbolic groups without
the unique product property. As an application, we obtain Tarski monster groups
without the unique product property.Comment: 22 page
- …