2014/06/05 by Bojan Mohar, Mohar, Bojan, Petr Škoda +1
Mathematics · #05C10 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C10
paper · pdf · doi:10.48550/arxiv.1406.1341
45 pages
arxiv created 2014/06/05 · arxiv updated 2014/06/06
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.