Intrinsic knotting and linking of complete graphs.
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 .
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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