The spherical genus and virtually planar graphs
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It is shown that G is virtually planar if and only if G is either planar or projective-planar and that sph( G ) = 1, 2 or ∞.About:
This article is published in Discrete Mathematics.The article was published on 1988-01-01 and is currently open access. It has received 38 citations till now. The article focuses on the topics: Polyhedral graph & Planar graph.read more
Citations
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Journal ArticleDOI
Random graph coverings i: general theory and graph connectivity
Alon Amit,Nathan Linial +1 more
TL;DR: A simple model for random graphs that have an n-fold covering map onto a fixed finite base graph and the main specific result is that if is the smallest vertex degree in G, then almost all n-covers of G are -connected.
Proceedings ArticleDOI
Random lifts of graphs
TL;DR: A simple probabilistic model for graphs that are lifts of a fixed base graph G, i.e., those graphs from which there is a covering man onto G, shows that almost every lift of G is δ(G)-connected.
Journal ArticleDOI
Forbidden Minors to Graphs with Small Feedback Sets
TL;DR: This paper characterize several families of graphs with small feedback sets, namely k1-FEEDback VERTEX SET, k2-FEedback EDGE SET and (k1;k2)FEEDBACK VERTex=EDGE SET, for small integer parameters k1 and k2.
Journal ArticleDOI
Generating Internally Four-Connected Graphs
Thor Johnson,Robin Thomas +1 more
TL;DR: It is proved that if H and G are internally 4-connected graphs such that they are not isomorphic, H is a minor of G, and they do not belong to a family of exceptional graphs, then there exists a graph H?
Journal ArticleDOI
On the Planar Split Thickness of Graphs
David Eppstein,Philipp Kindermann,Stephen G. Kobourov,Giuseppe Liotta,Anna Lubiw,Aude Maignan,Debajyoti Mondal,Hamideh Vosoughpour,Sue Whitesides,Stephen K. Wismath +9 more
TL;DR: The planar split thickness of a graph is the smallest k such that the graph is k-splittable into a planar graph as discussed by the authors, i.e., each vertex v is connected to at least one of the new vertices.
References
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Book ChapterDOI
Congruent Graphs and the Connectivity of Graphs
TL;DR: In this paper, the authors give conditions that two graphs be congruent and some theorems on the connectivity of graphs, and conclude with some applications to dual graphs, which can also be proved by topological methods.
Journal ArticleDOI
A kuratowski theorem for the projective plane
TL;DR: Let I ( S ) denote the set of graphs, each with no valency 2 vertices, which are irreducible for S, and using this notation the authors state Kuratowski's theorem.
Journal ArticleDOI
103 Graphs that are irreducible for the projective plane
Henry H. Glover,Henry H. Glover,John Philip Huneke,John Philip Huneke,Chin San Wang,Chin San Wang +5 more
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Uniqueness and faithfulness of embedding of toroidal graphs
TL;DR: The main theorems state that any 6-connected toroidal graph is uniquelly embeddable in a torus and that any6-connectedtoroidal graph with precisely three exceptions is faithfully embeddables in atorus.