On topologically frustrated polymers and where to find them

Abstract We prove the existence of graph-theoretic topological frustration in quasi-one-dimensional periodic bipartite lattices that are based on the two-dimensional honeycomb lattice. Then, we provide insights into how to construct such structures on the basis of the Tutte–Berge formula, Gallai–Edmonds theorem and quasi-symmetries. We notice an anomalous nullity in the graphs of such structures and suggest a possible explanation.