Reducing quadrangulations of the sphere and the projective plane [article]

Elke Fuchs, Laura Gellert
2017 arXiv   pre-print
We show that every quadrangulation of the sphere can be transformed into a 4-cycle by deletions of degree-2 vertices and by t-contractions at degree-3 vertices. A t-contraction simultaneously contracts all incident edges at a vertex with stable neighbourhood. The operation is mainly used in the field of t-perfect graphs. We further show that a non-bipartite quadrangulation of the projective plane can be transformed into an odd wheel by t-contractions and deletions of degree-2 vertices. We
more » ... that a quadrangulation of the projective plane is (strongly) t-perfect if and only if the graph is bipartite.
arXiv:1606.07662v3 fatcat:z2onopk4xvhezloj2elbuflere