Bojan Mohar, Petr Škoda
Published 2014-06-05Version 1
The structure of graphs with a 2-vertex-cut that are critical with respect to the Euler genus is studied. A general theorem describing the building blocks is presented. These constituents, called hoppers and cascades, are classified for the case when Euler genus is small. As a consequence, the complete list of obstructions of connectivity 2 for embedding graphs into the Klein bottle is obtained.
Excluded minors for the Klein Bottle I. Low connectivity case
Note on the Irreducible Triangulations of the Klein Bottle
The $K_{n+5}$ and $K_{3^2,1^n}$ families are obstructions to $n$-apex
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