Obstructions for embedding cubic graphs on the spindle surface

Authors:
Dan Archdeacon;C. Paul Bonnington
Affiliations:
Department of Mathematics and Statistics, University of Vermont, Burlington, VT;Department of Mathematics, University of Auckland, Private Bay 92019, Auckland, New Zealand
Venue:
Journal of Combinatorial Theory Series B
Year:
2004

Citing 6
Cited 0

A Kuratowski theorem for nonorientable surfaces

Journal of Combinatorial Theory Series B
Graph minors. VIII. A Kuratowski theorem for general surfaces

Journal of Combinatorial Theory Series B
The 2 and 3 representative projective planar embeddings

Journal of Combinatorial Theory Series B
Kuratowski-type theorems do not extend to pseudosurfaces

Journal of Combinatorial Theory Series B
On 3-regular graphs having crossing number at least 2

Journal of Graph Theory
Computing the orientable genus of projective graphs

Journal of Graph Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

The spindle surface S is the pinched surface formed by identifying two points on the sphere. In this paper we examine cubic graphs that minimally do not embed on the spindle surface. We give the complete list of 21 cubic graphs that form the topological obstruction set in the cubic order for graphs that embed on S.A graph G is nearly planar if there exists an edge e such that G-e is planar. We show that a cubic obstruction for near-planarity is the same as an obstruction for embedding on the spindle surface. Hence we also give the topological obstruction set for cubic nearly planar graphs.