We determine the list chromatic number of the square of a graph χl(G 2) in terms of its maximum degree ∆ when its maximum average degree, denoted mad(G), is sufficiently small. For ∆ ≥ 6, if mad(G) < 2 + 4∆−8 5∆+2 , then χl(G 2) = ∆ + 1. In particular, if G is planar with girth g ≥ 7 + 12 ∆−2 , then χl(G 2) = ∆ + 1. Under the same conditions, χil(G) = ∆, where χ i l is the list injective chroma...

Abstract We prove that the order of a finite group

A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index of a graph is the minimum number of colors needed to obtain a strong edge coloring. In an analogous way, we can define the list version of strong edge coloring and list version of strong chromatic index. In this paper we prove that if G is a graph with maximu...