Adjacent vertex distinguishing edge choosability of 1-planar graphs with maximum degree at least 23

Fora simple graph G, an adjacent vertex distinguishing edge k-coloring of G is a mapping phi: E(G) -> {1, 2, ... , k} such that phi(e(1)) not equal phi(e(2)) for every adjacent edges e(1) and e(2) in E(G) and C-phi(u) not equal C-phi(v) for each edge uv is an element of E(G), where C-phi(v) (or C-phi(u)) denotes the set of colors assigned to the edges incident with v (or u). For each edge e is an element of E(G), let L(e) be a list of possible colors that can be used on e. If, whenever we give a list assignment L = {L(e)vertical bar vertical bar L(e)vertical bar = k, e is an element of E(G)}, there exists an adjacent vertex distinguishing edge k-coloring phi such that phi(e) is an element of L(e) for each edge e is an element of E(G), then we say that phi is a list adjacent vertex distinguishing edge k-coloring. The smallest k for which such a coloring exists is called the adjacent vertex distinguishing edge choosability of G, denoted by ch '(a)(G). A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. There is almost no result yet about ch '(a)(G) if G is a 1-planar graph. We prove that ch '(a)(G) <= Delta + 3 for every 1-planar graph G with maximum degree Delta >= 23. (c) 2023 Elsevier B.V. All rights reserved.