Antiparallel d-stable traces and a stronger version of ore problem

作者：Rus Jernej^*

来源：Journal of Mathematical Biology, 2017, 75(1): 109-127.

DOI：10.1007/s00285-016-1077-2

• Double trace
• d-stable trace
• Strong trace
• Single face embedding
• Spanning tree
• Self-assembling
• Polypeptide nanostructure
• Strands of DNA

In 2013 a novel self-assembly strategy for polypeptide nanostructure design which could lead to significant developments in biotechnology was presented in Gradiar et al. (Nat Chem Bio 9:362-366, 2013). It was since observed that a polyhedron P can be realized by interlocking pairs of polypeptide chains if its corresponding graph G(P) admits a strong trace. It was since also demonstrated that a similar strategy can also be expanded to self-assembly of designed DNA (Koar, Nat commun 7:1-8, 2016). In this direction, in the present paper we characterize graphs which admit closed walk which traverses every edge exactly once in each direction and for every vertex v, there is no subset N of its neighbors, with , such that every time the walk enters v from N, it also exits to a vertex in N. This extends Thomassen's characterization (Thomassen, J Combin Theory Ser B 50:198-207, 1990) for the case .

• 出版日期2017-7