Outerplanar Graphs and Weak Duals
AbstractA 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  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.
How to Cite
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.