Planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable Original Research Article

The Total Coloring Conjecture, in short, TCC, says that every simple graph is image-totally-colorable where image is the maximum degree of the graph. Even for planar graphs this conjecture has not been completely settled yet. However, every planar graph with image has been proved to be image-totally-colorable. In this paper, we prove that planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable.