Outerplanar Graphs and Weak Duals

Authors

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

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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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.

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 https://www.informaticsjournals.com/index.php/jims/article/view/16694