A graph property is a set of (countable) graphs. A homomorphism from a
graph G to a graph H is an edge-preserving map from the vertex set of G into
the vertex set of H; if such a map exists, we write G → H. Given any graph
H, the hom-property →H is the set of H-colourable graphs, i.e., the set of
all graphs G satisfying G → H. A graph property P is of finite character if,
whenever we have that F ∈ P for every finite induced subgraph F of a graph
G, then we have that G ∈ P too. We explore some of the relationships of the
property attribute of being of finite character to other property attributes
such as being finitely-induced-hereditary, being finitely determined, and being
axiomatizable. We study the hom-properties of finite character, and prove
some necessary and some sufficient conditions on H for →H to be of finite
character. A notable (but known) sufficient condition is that H is a finite
graph, and our new model-theoretic proof of this compactness result extends
from hom-properties to all axiomatizable properties. In our quest to find an
intrinsic characterization of those H for which →H is of finite character,
we find an example of an infinite connected graph with no finite core and
chromatic number 3 but with hom-property not of finite character.
This thesis examines the concepts of copyright law and property within a digital setting, whilst focusing on the way that technology and law have influenced both copyright law and property law. In examining the relationship ...
Ndlovu, Talent Ndabenhle(University of Pretoria, 2016)
Using key informant interviews and a detailed household survey, this study compares Bela-Bela and Bjatladi Communal Property Associations (CPAs) across six categories of indicators known to facilitate sustainable collective ...