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 …

Mim-width and sim-width are among the most powerful graph width parameters, with sim-
width more powerful than mim-width, which is in turn more powerful than clique-width. While …

A colouring of a graph G=(V, E) is a mapping c: V→{1, 2,…} such that c (u)≠ c (v) for every
two adjacent vertices u and v of G. The List k-Colouring problem is to decide whether a …

The Colouring problem is to decide if the vertices of a graph can be coloured with at most k
colours for an integer k, such that no two adjacent vertices are coloured alike. A graph G is H …

For an integer t, we let P_t P t denote the t-vertex path. We write H+ G H+ G for the disjoint
union of two graphs H and G, and for an integer r and a graph H, we write rH for the disjoint …

For k≥ 1, a k-colouring c of G is a mapping from V (G) to {1, 2,…, k} such that c (u)≠ c (v) for
any two adjacent vertices u and v. The k-Colouring problem is to decide if a graph G has a k …

Abstract A function c: V (G) → {1, 2, ..., k\} c: V (G)→ 1, 2,…, k is ak-colouring of a graph G if c
(u) ≠ c (v) c (u)≠ c (v) whenever u and v are adjacent. If any two colour classes induce the …

For k ≥ 1 k≥ 1, ak-colouring c of G is a mapping from V (G) to {1, 2, ..., k\} 1, 2,…, k such that
c (u) ≠ c (v) c (u)≠ c (v) for any two non-adjacent vertices u and v. The k-Colouring problem …

Classifying k-edge colouring for H-free graphs - ScienceDirect Skip to main contentSkip to
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We prove that the class of $(K_t, sP_1+ P_5) $-free graphs has bounded mim-width for
every $ s\geq 0$ and $ t\geq 1$, and that there is a polynomial-time algorithm that, given a …