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On terminal delta-wye reducibility of planar graphs

Authors

  • Isidoro Gitler,

    1. Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Av. IPN 2508 Col. San Pedro Zacatenco, Apartado Postal 14–740, México, Distrito Federal, C. P. 07360
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  • Feliú Sagols

    Corresponding author
    1. Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Av. IPN 2508 Col. San Pedro Zacatenco, Apartado Postal 14–740, México, Distrito Federal, C. P. 07360
    • Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Av. IPN 2508 Col. San Pedro Zacatenco, Apartado Postal 14–740, México, Distrito Federal, C. P. 07360
    Search for more papers by this author

Abstract

We prove terminal Δ-Y reducibility of planar graphs with at most three terminals. The most important consequence of our proof is that this implicitly gives an efficient algorithm with time complexity O(|E(G)|4) for reducibility of planar graphs G with at most three terminals. It also can be used for restricted reducibility problems with more terminals. Our proof uses a very well-known translation from these operations to transformations on the medial graph. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(2), 174–186 2011

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