Reducing quadrangulations of the sphere and the projective plane
Combinatorics
2017-03-14 v3
Abstract
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.
Cite
@article{arxiv.1606.07662,
title = {Reducing quadrangulations of the sphere and the projective plane},
author = {Elke Fuchs and Laura Gellert},
journal= {arXiv preprint arXiv:1606.07662},
year = {2017}
}
Comments
10 pages, 4 figures, new results on quadrangulations of the sphere added, old results about $t$-perfection became corollaries