On edge colorings of 1-planar graphs without adjacent triangles

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. In this paper, it is proved that every 1-planar graph without adjacent triangles and with maximum degree Δ⩾8Δ⩾8 can be edge-colored with Δ colors.

► In the study we investigate the edge coloring of 1-planar graphs without adjacent triangles.
► It is conjectured that every 1-planar graph with Δ⩾8Δ⩾8 is of Class 1.
► This conjecture has been confirmed for 1-planar graphs without adjacent triangles.