摘要 : A colouring of a graph G = (V, E) is a mapping c: V → {1, 2, ....} such that c(u) ≠ c(v) if uv ∈ E; if |c(V)| ≤ k then c is a k-colouring. The COLOURING problem is that of testing whether a given graph has a k-colouring for some g... 展开 A colouring of a graph G = (V, E) is a mapping c: V → {1, 2, ....} such that c(u) ≠ c(v) if uv ∈ E; if |c(V)| ≤ k then c is a k-colouring. The COLOURING problem is that of testing whether a given graph has a k-colouring for some given integer k. If a graph contains no induced subgraph isomorphic to any graph in some family H, then it is called H-free. The complexity of COLOURING for H-free graphs with |H| = 1 has been completely classified. When |H| = 2, the classification is still wide open, although many partial results are known. We continue this line of research and forbid induced subgraphs {H_1, H_2}, where we allow H_1 to have a single edge and H_2 to have a single non-edge. Instead of showing only polynomial-time solvability, we prove that COLOURING on such graphs is fixed-parameter tractable when parameterized by |H_1| + |H_2|. As a by-product, we obtain the same result both for the problem of determining a maximum independent set and for the problem of determining a maximum clique. 收起