In this paper we survey results and open problems on the structure of additive and
hereditary properties of graphs. The important role of vertex partition problems, in particular …

For a simple graph H, a graph G is called H-colourable if there is a homomorphism from G to
H (a mapping f: V (G)→ V (H) such that uv∈ E (G) implies f (u) f (v)∈ E (H)). The class→ H of …

A set P of graphs is termed hereditary property if and only if it contains all subgraphs of any
graph G belonging to P. A graph is said to be maximal with respect to a hereditary property P …

A property of graphs is a non-empty set of graphs. A property P is called hereditary if every
subgraph of any graph with property P also has property P. Let P₁,..., Pₙ be properties of …

The study and recognition of graph families (or graph properties) is an essential part of
combinatorics. Graph colouring is another fundamental concept of graph theory that can be …

A graph property is any isomorphism closed class of simple graphs. For a simple finite graph
H, let→ H denote the class of all simple countable graphs that admit homomorphisms to H …

In this paper we translate Ramsey-type problems into the language of decomposable
hereditary properties of graphs. We prove a distributive law for reducible and decomposable …

For a graph H, we compare two notions of uniquely H-colourable graphs, where one is
defined via automorphisms, the second by vertex partitions. We prove that the two notions of …

EDGE-COLOURINGS AND HEREDITARY PROPERTIES OF GRAPHS THESIS PHILOSOPHIAE
DOCTOR MATHEMATICS FACULTY OF SCIENCE RAND AFRIKAANS UNI Page 1 …

In this paper, we investigate the problem of (k, Q)-Ramsey classes of graphs, which were
introduced in [M. Borowiecki, A. Fiedorowicz, On partitions of hereditary properties of graphs …