We show that there exist linear-time algorithms that compute the strong chromatic index and a maximum induced matching of treecographs when the decomposition tree is a part of the input. We also show that there exists an efficient algorithm for the strong chromatic index of permutation graphs.

The strong chromatic index of a graph G is the smallest integer k such that the edge set E( G) can be partitioned into k induced subgraphs of G which form matchings. In this paper we consider the behavior of the strong chromatic index of a sparse random graph K (n, p), where p = p(n) = 0(1).

The point-distinguishing chromatic index of a graph represents the minimum number of colours in its edge colouring such that each vertex is distinguished by the set of colours of edges incident with it. Asymptotic information on jumps of the point-distinguishing chromatic index of Kn,n is found.

In this note, multigraphs will have no loops. For a multigraph G, the least number of colours needed to colour the edges of G in such a way that no two edges on the same vertex of G have the same colour, is called the edge-chromatic number, or the chromatic index, of G. It is clear that if A(G) denotes the chromatic index of G, then A(G) <x'(G). If A(G) = x ' (G) , then G is said to be Class 1,...

In a Steiner triple system of order v, STS(v), a set of three lines intersecting pairwise in three distinct points is called a triangle. A set of lines containing no triangle is called triangle-free. The minimum number of triangle-free sets required to partition the lines of a Steiner triple system S, is called the triangle chromatic index of S. We prove that for all admissible v, there exists ...

an acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. the acyclic chromatic index of a graph $g$ denoted by $chi_a '(g)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. the maximum degree in $g$ denoted by $delta(g)$, is the lower bound for $chi_a '(g)$. $p$-cuts introduced in this paper acts as a powerfu...