The Möbius strip, also called the twisted cylinder (Henle 1994, p. . the Möbius strip can be colored using only six colors, as illustrated in Tietze's graph above.

A Möbius strip, Möbius band, or Möbius loop also spelled Mobius or Moebius, is a surface with .. In graph theory, the Möbius ladder is a cubic graph closely related to the Möbius strip. In 1968, Gonzalo Vélez Jahn (UCV, Caracas, Venezuela).

In graph theory, the Möbius ladder Mn is a cubic circulant graph with an even number n of because (with the exception of M6 = K3,3) Mn has exactly n/2 4- cycles which link together by their shared edges to form a topological Möbius strip.

I think you are confusing some concepts. A graph can be crossing free in some embeddings and not in others - think of a circle embedded as.