Abstract
In this work we consider the following problem. Given a planar graph G with maximum degree 4 and a function flex: \(E \longrightarrow {\mathbb{N}}_0\) that gives each edge a flexibility. Does G admit a planar embedding on the grid such that each edge e has at most flex(e) bends? Note that in our setting the combinatorial embedding of G is not fixed.
We give a polynomial-time algorithm for this problem when the flexibility of each edge is positive. This includes as a special case the problem of deciding whether G admits a drawing with at most one bend per edge.
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Bläsius, T., Krug, M., Rutter, I., Wagner, D. (2011). Orthogonal Graph Drawing with Flexibility Constraints. In: Brandes, U., Cornelsen, S. (eds) Graph Drawing. GD 2010. Lecture Notes in Computer Science, vol 6502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18469-7_9
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DOI: https://doi.org/10.1007/978-3-642-18469-7_9
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