Characterization and enumeration of toroidal K_{3,3}-subdivision-free graphs
Abstract
We describe the structure of 2-connected non-planar toroidal graphs with no K_{3,3}-subdivisions, using an appropriate substitution of planar networks into the edges of certain graphs called toroidal cores. The structural result is based on a refinement of the algorithmic results for graphs containing a fixed K_5-subdivision in [A. Gagarin and W. Kocay, "Embedding graphs containing K_5-subdivisions'', Ars Combin. 64 (2002), 33-49]. It allows to recognize these graphs in linear-time and makes possible to enumerate labelled 2-connected toroidal graphs containing no K_{3,3}-subdivisions and having minimum vertex degree two or three by using an approach similar to [A. Gagarin, G. Labelle, and P. Leroux, "Counting labelled projective-planar graphs without a K_{3,3}-subdivision", submitted, arXiv:math.CO/0406140, (2004)].
Keywords
Cite
@article{arxiv.math/0411356,
title = {Characterization and enumeration of toroidal K_{3,3}-subdivision-free graphs},
author = {Andrei Gagarin and Gilbert Labelle and Pierre Leroux},
journal= {arXiv preprint arXiv:math/0411356},
year = {2008}
}
Comments
18 pages, 7 figures and 4 tables