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Elimination of local bridges
 Math. Slovaca
, 1997
"... Let K be a subgraph of G. It is shown that if G is 3â€“connected modulo K then it is possible to replace branches of K by other branches joining same pairs of main vertices of K such that G has no local bridges with respect to the new subgraph K. A linear time algorithm is presented that either perfor ..."
Abstract

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Let K be a subgraph of G. It is shown that if G is 3â€“connected modulo K then it is possible to replace branches of K by other branches joining same pairs of main vertices of K such that G has no local bridges with respect to the new subgraph K. A linear time algorithm is presented that either performs such a task, or finds a Kuratowski subgraph K5 or K3,3 in a subgraph of G formed by a branch e and local bridges on e. This result is needed in linear time algorithms for embedding graphs in surfaces.