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Obstructions for the Disk and the Cylinder Embedding Extension Problems

Published online by Cambridge University Press:  12 September 2008

Bojan Mohar
Bojan Mohar
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 61111 Ljubljana, Slovenia email: bojan.mohar@uni-lj.si
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Abstract

Let S be a closed surface with boundary ∂S and let G be a graph. Let K ⊆ G be a subgraph embedded in S such that ∂S ⊆ K. An embedding extension of K to G is an embedding of G in S that coincides on K with the given embedding of K. Minimal obstructions for the existence of embedding extensions are classified in cases when S is the disk or the cylinder. Linear time algorithms are presented that either find an embedding extension, or return an obstruction to the existence of extensions. These results are to be used as the corner stones in the design of linear time algorithms for the embeddability of graphs in an arbitrary surface and for solving more general embedding extension problems.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 3 , September 1994 , pp. 375 - 406
Copyright
Copyright © Cambridge University Press 1994

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