A (P3-free, K3-free)-colouring of a graph G = (V, E) is a partition of V = A âˆª B such that G[A] is P3-free and G[B] is K3-free. This problem is known to be NP-complete even when restricted to planarâ€¦ (More)

The Near-Bipartiteness problem is that of deciding whether or not the vertices of a graph can be partitioned into sets A and B, where A is an independent set and B induces a forest. The set A in suchâ€¦ (More)

We continue research into a well-studied family of problems that ask whether the vertices of a graph can be partitioned into sets A and B, where A is an independent set and B induces a graph fromâ€¦ (More)

Let G be a graph with a vertex colouring Î±. Let a and b be two colours. Then a connected component of the subgraph induced by those vertices coloured either a or b is known as a Kempe chain. Aâ€¦ (More)

Given a graph G = (V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempeâ€¦ (More)

This paper investigates the computational complexity of deciding whether the vertices of a graph can be partitioned into a disjoint union of cliques and a triangle-free subgraph. This problem isâ€¦ (More)

The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer k â‰¥ 0, to delete at most k vertices from a given graph so that what remains is aâ€¦ (More)