Paper extends Enami-Ozeki-Yamaguchi's work on planar quadrangulations.
problem Finding the maximum number of colors for proper anti-rainbow colorings on planar quadrangulations.
method Introducing half-monochromatic colorings for plane graphs with even polygonal faces and providing an upper bound in terms of the independence number.
result An upper bound on the maximum number of colors for half-monochromatic colorings is given in terms of the independence number.