A Sufficient Condition for an IC-Planar Graph to be Class 1.

Two distinct crossings are independent if the end-vertices of any two pairs of crossing edges are disjoint. A graph said to be plane graph with independent crossings or IC-planar, if it can be drawn in the plane such that every two crossings are independent. In this paper, we proved that every IC-planar graph G with Δ (G) = 7 admits a proper edge-coloring with Δ (G) colors if G does not contain a 6-cycle with three chords. [ABSTRACT FROM AUTHOR]