Signed planar graphs with ?? 8 are ?-edge-colorable

A well-known theorem due to Vizing states that every graph with maximum degree A is A-or (A + 1) -edge-colorable. Recently, Behr extended the concept of edge coloring in a natural way to signed graphs. He also proved that an analogue of Vizing's Theorem holds for all signed graphs. Adopting Behr's definition, Zhang et al. proved that a signed planar graph G with maximum degree A is A -edge-colorable if either A >= 10 or A is an element of {8, 9} and G contains no adjacent triangles. They also proposed the conjecture that every signed planar graph with A >= 6 is A -edge-colorable, as a generalization of Vizing's Planar Graph Conjecture. In this paper, we prove that every signed planar graph with A >= 8 is A -edge -colorable.(c) 2023 Elsevier B.V. All rights reserved.