Can the vertices of a graph $ G $ be partitioned into $ A\cup B $, so that $ G [A] $ is a line-
graph and $ G [B] $ is a forest? Can $ G $ be partitioned into a planar graph and a perfect …

For graph classes\wp_1,...,\wp_k, Generalized Graph Coloring is the problem of deciding
whether the vertex set of a given graph G can be partitioned into subsets V_1,..., V_k so that …

The generalized graph colouring problem (GCOL) for a fixed integer k, and fixed classes of
graphs P_1,..., P_k (usually describing some common graph properties), is to decide, for a …

Let (L a,⊆) be the lattice of hereditary and additive properties of graphs. A reducible
property R∈ L a is called minimal reducible bound for a property P∈ L a if in the interval (P …

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 …

An Erratum has been published for this article in Journal of Graph Theory 50: 261, 2005. A
graph property (ie, a set of graphs) is hereditary (respectively, induced‐hereditary) if it is …

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 …

An additive hereditary property of graphs is any class of simple graphs which is closed
under unions, subgraphs and isomorphisms. The set of all such properties is a lattice with …

An additive hereditary graph property is a set of graphs, closed under isomorphism and
under taking subgraphs and disjoint unions. Let ${\cal P} _1,>...,{\cal P} _n $ be additive …

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 …