Checkerboard embeddings of *-graphs into nonorientable surfaces
Abstract
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of nonorientable surfaces into which such graphs may be embedded. In a previous paper by the authors, the problem of calculating whether a given *-graph in which all vertices have degree 4 or 6 admits a Z2-homologically trivial embedding into a given orientable surface was shown to be equivalent to a problem on matrices. Here we extend those results to nonorientable surfaces. The embeddability condition that we obtain yields quadratic-time algorithms to determine whether a *-graph with all vertices of degree 4 or 6 admits a Z2-homologically trivial embedding into the projective plane or into the Klein bottle.
Cite
@article{arxiv.1312.6342,
title = {Checkerboard embeddings of *-graphs into nonorientable surfaces},
author = {Tyler Friesen and Vassily Olegovich Manturov},
journal= {arXiv preprint arXiv:1312.6342},
year = {2014}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1212.5646