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Article
Projective-planar graphs with no K3,4-minor. II.
Journal of Graph Theory
Document Type
Article
Publication Date
12-1-2016
Disciplines
Abstract
The authors previously published an iterative process to generate a class of projectiveplanar K3,4-free graphs called ‘patch graphs’. They also showed that any simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a subgraph of a patch graph. In this paper, we describe a simpler and more natural class of cubic K3,4- free projective-planar graphs which we call M¨obius hyperladders. Furthermore, every simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a minor of a M¨obius hyperladder. As applications of these structures we determine the page number of patch graphs and of M¨obius hyperladders.
DOI
10.1002/jgt.22113
Citation Information
John Maharry and Dan Slilaty. "Projective-planar graphs with no K3,4-minor. II." Journal of Graph Theory Vol. 86 Iss. 1 (2016) p. 92 - 103 ISSN: 0364-9024 Available at: http://works.bepress.com/dan_slilaty/18/