For a positive integer k, ak‐coloring of a graph is a mapping such that whenever. The
Coloring problem is to decide, for a given G and k, whether ak‐coloring of G exists. If k is …

A graph is H-free if it does not contain an induced subgraph isomorphic to H. We denote by
P t and C t the path and the cycle on t vertices, respectively. In this paper, we prove that 4 …

The class of H-free graphs has bounded clique-width if and only if H is an induced subgraph
of the 4-vertex path P_4. We study the (un) boundedness of the clique-width of graph …

Let P t and C ℓ denote a path on t vertices and a cycle on ℓ vertices, respectively. In this
paper we study the k-coloring problem for (P t, C ℓ)-free graphs. Bruce et al.(2009), and …

The task of complete complexity dichotomy is to clearly distinguish between easy and hard
cases of a given problem on a family of subproblems. We consider this task for some …

If a graph G contains no subgraph isomorphic to some graph H, then G is called H-free. A
coloring of a graph G=(V, E) is a mapping c: V→{1, 2,…} such that no two adjacent vertices …

The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k
colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each …

A (proper) colouring is acyclic, star, or injective if any two colour classes induce a forest, star
forest or disjoint union of vertices and edges, respectively. Hence, every injective colouring …

The biclique problem asks, given a graph G and a parameter k, whether G has a complete
bipartite subgraph of k vertices in each part (a biclique of order k). Fixed-parameter …

The k-Coloring problem is to decide whether a graph can be colored with at most k colors
such that no two adjacent vertices receive the same color. The List k-Coloring problem …