## Abstract Let __G__ be a 3βconnected planar graph and __G__^\*^ be its dual. We show that the pathwidth of __G__^\*^ is at most 6 times the pathwidth of __G__. We prove this result by relating the pathwidth of a graph with the cutβwidth of its medial graph and we extend it to bounded genus embedd
Flexibility of Polyhedral Embeddings of Graphs in Surfaces
β Scribed by Bojan Mohar; Neil Robertson
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 296 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
In a 1973 paper, Cooke obtained an upper bound on the possible connectivity of a graph embedded in a surface (orientable or nonorientable) of fixed genus. Furthermore, he claimed that for each orientable genus #>0 (respectively, nonorientable genus #Γ >0, #Γ {2) there is a complete graph of orientab
In this article, we show that there exists an integer k(Ξ£)
## Abstract Current graphs and a theorem of White are used to show the existence of almost complete regular bipartite graphs with quadrilateral embeddings conjectured by Pisanski. Decompositions of __K~n~__ and __K~n, n~__ into graphs with quadrilateral embeddings are discussed, and some thickness