2026-07-25T11:56:11Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12954 2024-03-06T10:51:10Z ddc:004 open_access

The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes Mohammed, Abdulmelik Jonoska, Nataša Saito, Masahico DNA origami Scaffold routing Graphs Surfaces Knots Eulerian circuits The routing of a DNA-origami scaffold strand is often modelled as an Eulerian circuit of an Eulerian graph in combinatorial models of DNA origami design. The knot type of the scaffold strand dictates the feasibility of an Eulerian circuit to be used as the scaffold route in the design. Motivated by the topology of scaffold routings in 3D DNA origami, we investigate the knottedness of Eulerian circuits on surface-embedded graphs. We show that certain graph embeddings, checkerboard colorable, always admit unknotted Eulerian circuits. On the other hand, we prove that if a graph admits an embedding in a torus that is not checkerboard colorable, then it can be re-embedded so that all its non-intersecting Eulerian circuits are knotted. For surfaces of genus greater than one, we present an infinite family of checkerboard-colorable graph embeddings where there exist knotted Eulerian circuits. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Abdulmelik Mohammed and Nataša Jonoska and Masahico Saito 2020 Is Part Of LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DNA.2020.1 urn:nbn:de:0030-drops-129540 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.1 eng https://creativecommons.org/licenses/by/3.0/legalcode