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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 3–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 ..."
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Cited by 8 (8 self)
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Let K be a subgraph of G. It is shown that if G is 3–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.
Obstructions for 2Möbius band embedding extension problem
 SIAM J. Discrete Math
, 1997
"... Abstract. Let K = C ∪ e1 ∪ e2 be a subgraph of G, consisting of a cycle C and disjoint paths e1 and e2, connecting two interlacing pairs of vertices in C. Suppose that K is embedded in the MöbiusbandinsuchawaythatC lies on its boundary. An algorithm is presented which in linear time extends the embe ..."
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Cited by 3 (3 self)
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Abstract. Let K = C ∪ e1 ∪ e2 be a subgraph of G, consisting of a cycle C and disjoint paths e1 and e2, connecting two interlacing pairs of vertices in C. Suppose that K is embedded in the MöbiusbandinsuchawaythatC lies on its boundary. An algorithm is presented which in linear time extends the embedding of K to an embedding of G, if such an extension is possible, or finds a “nice ” obstruction for such embedding extensions. The structure of obtained obstructions is also analysed in details. Key words. surface embedding, obstruction, Möbius band, algorithm AMS subject classifications. 05C10, 05C85, 68Q20 1. Introduction. Let K be a subgraph of a graph G. A Kbridge (or a Kcomponent)inG is a subgraph of G which is either an edge e ∈ E(G)\E(K) (together with its endpoints) which has both endpoints in K, or it is a connected component of G − V (K) together with all edges (and their endpoints) between this component and K. EachedgeofaKbridge B having an endpoint in K is a foot of B. The vertices