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Fold-2-covering triangular embeddings

✍ Scribed by D. Bénard; A. Bouchet; R. B. Richter

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
143 KB
Volume
43
Category
Article
ISSN
0364-9024

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✦ Synopsis

For a graph G and a positive integer m, G (m) is the graph obtained from G by replacing every vertex by an independent set of size m and every edge by m 2 edges joining all possible new pairs of ends. If G triangulates a surface, then it is easy to see from Euler's formula that G (m) can, in principle, triangulate a surface. For m prime and at least 7, it has previously been shown that in fact G (m) does triangulate a surface, and in fact does so as a ''covering with folds'' of the original triangulation. For m ¼ 5, this would be a consequence of Tutte's 5-Flow Conjecture. In this work, we investigate the case m ¼ 2 and describe simple classes of triangulations G for which G (2) does have a triangulation that covers G ''with folds,'' as well as providing a simple infinite class of triangulations G of the sphere for which G (2) does not triangulate any surface.

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