Geodesic
Acyclic chromatic index of IC-planar graphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 965-978

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Two distinct crossings are independent if the end-vertices of any two pairs of crossing edges are disjoint. If a graph G has a drawing in the plane such that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G is the least number of colors such that G has an acyclic edge coloring and denoted by χ_a^'(G). In this paper, we prove that χ_a^'(G)≤Δ(G)+17, for any IC-planar graph G with maximum degree Δ(G).
Keywords: acyclic chromatic index, maximum degree, IC-planar graph 
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Song, Wenyao; Miao, Lianying; Zhao, Yueying; Zhu, Haiyang. Acyclic chromatic index of IC-planar graphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 965-978. http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a5/