The structure and labelled enumeration of K_{3,3}-subdivision-free projective-planar graphs
Abstract
We consider the class F of 2-connected non-planar K_{3,3}-subdivision-free graphs that are embeddable in the projective plane. We show that these graphs admit a unique decomposition as a graph K_5 (the core) where the edges are replaced by two-pole networks constructed from 2-connected planar graphs. A method to enumerate these graphs in the labelled case is described. Moreover, we enumerate the homeomorphically irreducible graphs in F and homeomorphically irreducible 2-connected planar graphs. Particular use is made of two-pole directed series-parallel networks. We also show that the number m of edges of graphs in F with n vertices satisfies the bound m <=3n-6, for n >= 6.
Keywords
Cite
@article{arxiv.math/0406140,
title = {The structure and labelled enumeration of K_{3,3}-subdivision-free projective-planar graphs},
author = {Andrei Gagarin and Gilbert Labelle and Pierre Leroux},
journal= {arXiv preprint arXiv:math/0406140},
year = {2010}
}
Comments
Revised version. 20 pages. To appear in Pure Mathematics and Applications - Algebra and Theoretical Computer Science