Computing Invariants of Knotted Graphs Given by Sequences of Points in 3-Dimensional Space

Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


We design a fast algorithm for computing the fundamental group of the complement to any knotted polygonal graph in 3-space. A polygonal graph consists of straight segments and is given by sequences of vertices along edge-paths. This polygonal model is motivated by protein backbones described in the Protein Data Bank by 3D positions of atoms. Our KGG algorithm simplifies a knotted graph and computes a short presentation of the Knotted Graph Group containing powerful invariants for classifying graphs up to isotopy. We use only a reduced plane diagram without building a large complex representing the complement of a graph in 3-space.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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