The half-monochromatic colorings of plane graphs with even polygonal faces

On the maximum number of colors for proper anti-rainbow colorings on a planar quadrangulation, an upper bound was given by Enami-Ozeki-Yamaguchi in terms of the independence number. In this paper, as an extension, we introduce the half-monochromatic coloring on a plane graph with even polygonal faces, and give an upper bound on the maximum number of colors for such colorings in terms of the independence number.