All face 2-colorable d-angulations are Grünbaum colorable
Lawrencenko, Serge · Magomedov, Abdulkarim M.
Original · EN
A d-angulation of a surface is an embedding of a 3-connected graph on that surface that divides it into d-gonal faces. A d-angulation is said to be Grünbaum colorable if its edges can be d-colored so that every face uses all d colors. Up to now, the concept of Grünbaum coloring has been related only to triangulations (d = 3), but in this note, this concept is generalized for an arbitrary face size d 3. It is shown that the face 2-colorability of a d-angulation P implies the Grünbaum colorability of P. Some wide classes of triangulations have turned out to be face 2-colorable.
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