Entire Chromatic Number and Entire Coloring Algorithms of Regular Planar Meshes

In this paper, we propose three entire coloring schemes for regular planar meshes — square meshes, hexagonal meshes and honeycomb meshes, respectively. Based on these schemes, we propose three efficient entire coloring algorithms for these three planar meshes and prove that the entire chromatic number of square meshes is 7 (maximum degree plus 3), the entire chromatic number of hexagonal meshes is 9 (maximum degree plus 2), and the entire chromatic number of honeycomb meshes is 7 (maximum degree plus 4).