Abstract
Many practical applications demand additional restrictions on an admissible planar embedding. In particular, constraints on the permitted (clockwise) order of the edges around a vertex, like so-called side constraints, abound. In this paper, we introduce a set of hierarchical embedding constraints that also comprises side constraints. We present linear time algorithms for testing if a graph is ec-planar, i.e., admits a planar embedding satisfying the given embedding constraints, as well as for computing such an embedding. Moreover, we characterize the set of all possible ec-planar embeddings and consider the problem of finding a planar combinatorial embedding of a planar graph such that an additional edge can be inserted with the minimum number of crossings; we show that this problem can still be solved in linear time under the additional restrictions of embedding constraints.
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Gutwenger, C., Klein, K., Mutzel, P. (2007). Planarity Testing and Optimal Edge Insertion with Embedding Constraints. In: Kaufmann, M., Wagner, D. (eds) Graph Drawing. GD 2006. Lecture Notes in Computer Science, vol 4372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70904-6_14
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DOI: https://doi.org/10.1007/978-3-540-70904-6_14
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