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

Dainis Zeps (1)

1 IMCS - Institute of Mathematics and Computer Science

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 single common graph that can be received as edge sum modulo two of the octahedron graph O and the minimal wheel W3. 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 Grötzsch class, received applying Mycielski's Construction to odd cycle.

Mots clés: graph coloring; chromatic critical graphs; wheels; planar graphs; projective planar graphs; Grotzsh graph; Mycielski's construction

Domaines: Combinatoire [math.CO]

Dainis Zeps. On building 4-critical plane and projective plane multiwheels from odd wheels. 2012. ⟨hal-00672711⟩