Over the past decade, many major advances have been made in the field of graph colouring
via the probabilistic method. This monograph provides an accessible and unified treatment …

We define the incidence coloring number of a graph and bound it in terms of the maximum
degree. The incidence coloring number turns out to be the strong chromatic index of an …

A Bound on the Strong Chromatic Index of a Graph Page 1 Journal of Combinatorial Theory,
Series B TB1724 journal of combinatorial theory, Series B 69, 103 109 (1997) A Bound on the …

We develop an improved bound for the chromatic number of graphs of maximum degree Δ
under the assumption that the number of edges spanning any neighbourhood is at most for …

arXiv:2210.05915v2 [math.CO] 22 Apr 2023 Page 1 arXiv:2210.05915v2 [math.CO] 22 Apr
2023 Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) …

In this paper we consider the approximability of the maximum induced matching problem
(MIM). We give an approximation algorithm with asymptotic performance ratio d− 1 for MIM …

A strong edge-coloring of a graph $ G $ is a coloring of the edges such that every color class
induces a matching in $ G $. The strong chromatic index of a graph is the minimum number …

We prove χ′ s (G)≤ 1.93 Δ (G) 2 for graphs of sufficiently large maximum degree where χ′
s (G) is the strong chromatic index of G. This improves an old bound of Molloy and Reed. As …

We prove χ s′(G)≤ 1.93 Δ (G) 2 for graphs of sufficiently large maximum degree where χ
s′(G) is the strong chromatic index of G. This improves an old bound of Molloy and Reed …

Packing a maximum number of disjoint triangles into a given graph G is NP-hard, even for
most classes of structured graphs. In contrast, we show that packing a maximum number of …