Outerplanar Graphs and Weak Duals

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Authors

  • Herbert J. Fleischner
     Institute for Advanced Study ,IN
  • Dennis P. Geller
     Austrian Academy of Sciences, SUNY at Binghamton ,US
  • Frank Harary
     University of Oxford ,GB

Abstract

A planar graph is outer planar if it can be embedded irr the plane so that every point lies on the exterior region. Outerplanar graphs were characterized by Chartrand and Harary [1] as those graphs containing subgraphs homeomorphic onto K4 or K2,3. In this paper we present an alternate characterization of outerplanar graphs in terms of duals, and discuss some relationships between the degrees of the points of outerplanar graphs and the lengths of the boundaries of their interior regions.

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Published

1974-12-01

How to Cite

Fleischner, H. J., Geller, D. P., & Harary, F. (1974). Outerplanar Graphs and Weak Duals. The Journal of the Indian Mathematical Society, 38(1-4), 215–219. Retrieved from http://www.informaticsjournals.com/index.php/jims/article/view/16694

Issue

Volume 38, Issue 1-4, March-December 1974

Section

Articles

License

Copyright (c) 1974 Herbert J. Fleischner, Dennis P. Geller, Frank Harary

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

G. CHARTRAND and F. HARARY, Planar permutation graphs, Ann. Inst. Hem Poincare Sec. B, 3(1967), 433-438.

H.S.M. COXETER, The four-colour map problem. 1840-1890, Math. Teacher 52 (1959), 283-289.

F. HARARY. Graph Theory, Addison-Wesley, Reading, 1969.

H. WHITNEY, Non-separable and planar graphs, Trans. Amer. Math. Soc. 34 (1932), 339-362.