On building 4-critical plane and projective plane multiwheels from odd wheels

Abstract

We build unbounded classes of plane and projective plane multiwheels that are 4-critical that are received summing odd wheels as edge sums modulo two. These classes can be considered as ascending from a single common graph that can be received as an edge sum modulo two of the octahedron graph O and the minimal wheel W_3. All graphs of these classes belong to 2n-2-edges-class of graphs, among which are those that quadrangulate projective plane, i.e., graphs from the Grötzsch class received applying Mycielski's Construction to an odd cycle.