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 …

It is proved that a graph with maximum degree at most 3 has a strong edge-colouring with at
most 10 colours. A simple algorithm achieving a strong edge-colouring with at most 10 …

In this paper, we show that the edge set of a cubic graph can always be partitioned into 10
subsets, each of which induces a matching in the graph. This result is a special case of a …

We show that the co-chordal cover number of a graph 𝐺 gives an upper bound for the
Castelnuovo-Mumford regularity of the associated edge ideal. Several known combinatorial …

Let G be a graph with chromatic number χ, maximum degree Δ and clique number ω. Reed's
conjecture states that χ≤⌈(1− ε)(Δ+ 1)+ ε ω⌉ for all ε≤ 1/2. It was shown by King and Reed …

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 …

In the strong edge coloring problem, the objective is to color the edges of the given graph
with the minimum number of colors so that every color class is an induced matching. In this …