Existence of Polyhedral Embeddings of Graphs
β Scribed by Bojan Mohar
- Publisher
- Springer-Verlag
- Year
- 2001
- Tongue
- English
- Weight
- 142 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0209-9683
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## 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
We give various conditions on pinched-torus polyhedral maps which are necessary for their graphs to be embeddable in the projective plane. Our other main result is that even if the graph of a polyhedral map in the pinched torus is embeddable in a projective plane, the map induced by the embedding ca