Symmetries of Möbius Ladders.
Topological Complexity in Protein Structures
For DNA molecules, topological complexity occurs exclusively as the result of knotting or linking of the polynucleotide backbone. By contrast, while a few knots and links have been found within the polypeptide backbones of some protein structures, non-planarity can also result from the connectivity between a polypeptide chain and inter- and intra-chain linking via cofactors and disulfide bonds. In this article, we survey the known types of knots, links, and non-planar graphs in protein structures...
Intrinsic linking and knotting are arbitrarily complex
We show that, given any n and α, any embedding of any sufficiently large complete graph in ℝ³ contains an oriented link with components Q₁, ..., Qₙ such that for every i ≠ j, and , where denotes the second coefficient of the Conway polynomial of .
Intrinsic knotting and linking of complete graphs.
Symmetries of embedded complete bipartite graphs
We characterize which automorphisms of an arbitrary complete bipartite graph can be induced by a homeomorphism of some embedding of the graph in S³.
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