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- Title
On nonplanarity of cubic graphs.
- Authors
Plachta, L.
- Abstract
A cubic graph is nonplanar if and only if it contains a subgraph homeomorphic to K. For a given 2-connected cubic graph G, let ed( G) denote the minimum number of edges such that, after their removal from G, the resulting graph becomes planar and let g( G) denote the genus of G . Moreover, for a given simple graph G, let cr( G) denote the minimum number of crossings of edges needed to draw G on the plane (the minimum is taken over all submersions of G in the plane). We study relations between the characteristics ed( G), g( G), and cr( G) for some special classes of graphs and discuss problems related to their evaluation.
- Subjects
GRAPH theory; HOMEOMORPHISMS; SUBGRAPHS; SUBMERSIONS (Mathematics); PROBLEM solving
- Publication
Journal of Mathematical Sciences, 2012, Vol 187, Issue 5, p545
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-012-1082-y