Abstract
This paper describes a linear time algorithm to determine whether an arbitrary graph is outerplanar. The algorithm uses an edge coloring technique and deletes successively vertices of degree less than or equal to two. If the degree of a vertex is two, both neighbors of the vertex are joined by an edge. The algorithm works without splitting the graph into its biconnected components or using bucket sort to give the adjacency lists a special order.
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Brehaupt, W.W., An efficient outerplanarity algorithm, Proc. 8th S.-E. Conf. on Combinatorics, Graph Theory and Computing, Lousiana State University, Feb. 1977.
Chartrand, G. and F. Harary, Planar permutation graphs, Ann. Inst. Henri Poincare, Vol. III 4(1967), 433–438.
Dirac, G.A., A property of 4-chromatic graphs, Fund. Math., 40(1953), 42–55.
Dirac, G.A. and S. Schuster, A theorem of Kuratowski, Indag. Math., 16(1954), 343–348.
Hopcroft, J.E. and R.E. Tarjan, Efficient planarity testing, J. ACM 21, 4(1974), 549–568.
Mitchell, S.L., Linear algorithms recognize outerplanar and maximal outerplanar graphs, Information processing letters, 9(1979), 229–232.
Syslo, M.M. and M. Iri, Efficient outerplanarity testing, Annales socientatis mathematica Polanae, Series IV: Fundamenta Informaticae, II(1979), 261–275.
Vo, K.-P., Determining outerplanarity using segment graphs, Linear and Multilinear Algebra, 13(1983), 333–343.
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© 1987 Springer-Verlag Berlin Heidelberg
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Wiegers, M. (1987). Recognizing outerplanar graphs in linear time. In: Tinhofer, G., Schmidt, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1986. Lecture Notes in Computer Science, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17218-1_57
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DOI: https://doi.org/10.1007/3-540-17218-1_57
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17218-5
Online ISBN: 978-3-540-47415-9
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