1 research outputs found
Reducing quadrangulations of the sphere and the projective plane
We show that every quadrangulation of the sphere can be transformed into a
-cycle by deletions of degree- vertices and by -contractions at
degree- vertices. A -contraction simultaneously contracts all incident
edges at a vertex with stable neighbourhood. The operation is mainly used in
the field of -perfect graphs. We further show that a non-bipartite
quadrangulation of the projective plane can be transformed into an odd wheel by
-contractions and deletions of degree- vertices. We deduce that a
quadrangulation of the projective plane is (strongly) -perfect if and only
if the graph is bipartite.Comment: 10 pages, 4 figures, new results on quadrangulations of the sphere
added, old results about -perfection became corollarie