On topologically frustrated polymers and where to find them

We prove the existence of graph-theoretic topological frustration in the 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.