# Extensions on 2-edge connected 3-regular up-embeddable graphs

Extensions on 2-edge connected 3-regular up-embeddable graphs It is known(5) that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the up-embeddability are known on the 3-regular graphs. LetG be a 2-edge connected 3-regular graph. We prove thatG is up-embeddable if and only ifG can be obtained from the graphs ϑ, $$\widetilde\theta$$ orK 4 by a series ofM- orN-extensions. Meanwhile, we also present a new structural characterization of such graphG provided thatG is up-embeddable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Extensions on 2-edge connected 3-regular up-embeddable graphs

, Volume 14 (4) – Jul 4, 2007
10 pages

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Publisher
Springer Journals
Copyright
Copyright © 1998 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02683816
Publisher site
See Article on Publisher Site

### Abstract

It is known(5) that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the up-embeddability are known on the 3-regular graphs. LetG be a 2-edge connected 3-regular graph. We prove thatG is up-embeddable if and only ifG can be obtained from the graphs ϑ, $$\widetilde\theta$$ orK 4 by a series ofM- orN-extensions. Meanwhile, we also present a new structural characterization of such graphG provided thatG is up-embeddable.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 4, 2007

### References

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