A property of graphs is any class of graphs closed under isomorphism. A property of graphs is induced-hereditary and additive if it is closed under taking induced subgraphs and disjoint unions of… (More)

For a simple 5nite graph G let Co(G) and Ce(G) denote the set of odd cycle lengths and even cycle lengths in a graph G, respectively. We will show that the chromatic number (G) of G satis5es:… (More)

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 the existence of… (More)

Let IL be the set of all hereditary and additive properties of graphs. For P1,P2 ∈ IL, the reducible property R = P1 ◦ P2 is defined as follows: G ∈ R if and only if there is a partition V (G) = V1 ∪… (More)

A hereditary property of graphs is any class of graphs closed under isomorphism and subgraphs. Let P1,P2, . . . ,Pn be hereditary properties of graphs. We say that a graph G has property P1◦P2◦ · · ·… (More)

In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental… (More)

For k 2 0, a graph G is called k-degenerate if every sub-graph of G +as a vertex of degree at most k. The Lick-White vertex partition rzumber, denoted p,JG), is the minimum number of colours required… (More)