Abstract
A linear-time algorithm that does not need a planar embedding is presented for the problem of computing two vertex-disjoint paths, each with prescribed endpoints, in an undirected 3-connected planar graph.
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References
Fortune, S., Hopcroft, J., Wyllie, J.: The directed subgraph homeomorphism problem. Theoret. Comput. Sci. 10, 111–121 (1980)
Harary, F.: Graph Theory. Addison-Wesley, Reading, Mass (1969)
Kramer, M.R., van Leeuwen, J.: The complexity of wire-routing and finding minimum area layouts for arbitrary VLSI circuits. In: Preparata, F.P. (ed.) Advances in Computing Research, vol. 2, pp. 129–146. JAI Press, Greenwich, Conn (1984)
Lynch, J.F.: The equivalence of theorem proving and the interconnection problem. ACM SIGDA Newsletter 5, 31–36 (1975)
Perković, L., Reed, B.: An improved algorithm for finding tree decompositions of small width. Internat. J. Foundat. Comput. Sci. 11, 365–371 (2000)
Perl, Y., Shiloach, Y.: Finding two disjoint paths between two pairs of vertices in a graph. J. ACM 25, 1–9 (1978)
Robertson, N., Seymour, P.D.: Graph Minors. XIII. The disjoint paths problem. J. Comb. Theory, Ser. B 63, 65–110 (1995)
Schrijver, A.: Finding k disjoint paths in a directed planar graph. SIAM J. Comput. 23, 780–788 (1994)
Shiloach, Y.: A polynomial solution to the undirected two paths problem. J. ACM 27, 445–456 (1980)
Tholey, T.: Solving the 2-disjoint paths problem in nearly linear time. Theory Comput. Systems 39, 51–78 (2006)
Woeginger, G.: A simple solution to the two paths problem in planar graphs. Inform. Process. Lett. 36, 191–192 (1990)
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Hagerup, T. (2007). A Very Practical Algorithm for the Two-Paths Problem in 3-Connected Planar Graphs. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_14
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DOI: https://doi.org/10.1007/978-3-540-74839-7_14
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