An injective k-edge-coloring of a graph G is an assignment of colors, ie integers in {1,…, k},
to the edges of G such that any two edges each incident with one distinct endpoint of a third …

A strong edge-colouring of a graph G is a proper edge-colouring such that every path of
length 3 uses three different colours. In this paper we improve some previous results on the …

Let Δ≥ 4 be an integer. We prove that every planar graph with maximum degree Δ and girth
at least 10Δ+ 46 is strong (2Δ− 1)-edge-colorable, that is best possible (in terms of number …

The strong chromatic index χ s′(G) of a graph G is the smallest integer k such that G has a
proper edge k-colouring with the condition that any two edges at distance at most 2 receive …

An induced matching in a graph is a set of edges whose endpoints induce a 1‐regular
subgraph. It is known that every n‐vertex graph has at most maximal induced matchings …

A matching M in a graph G is said to be an induced matching (2-matching, strong matching,
distance 2 matching) if no two edges of M are joined by an edge. A graph G is said to be well …

A strong edge coloring of a graph is a proper edge coloring such that no edge has two
incident edges of the same color. Erdős and Nešetřil conjectured in 1989 that 5 4 Δ 2 colors …

An incidence in a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G
incident to v. Two incidences (v, e) and (u, f) are adjacent if at least one of the following …

Only simple graphs are considered in this paper unless otherwise stated. Let G be a graph
with vertex set V (G), edge set E (G), minimum degree δ (G), and maximum degree∆(G)(for …

A matching in a graph is uniquely restricted if no other matching covers exactly the same set
of vertices. This notion was defined by Golumbic, Hirst, and Lewenstein and studied in a …