On the existence of multiply connected monolayered cyclofusenes with given parameters

摘要

For a given bipartite graph G its skewness is defined as the difference between the sizes of its classes of bipartition. We show that a multiply connected monolayered cyclofusene with m ≥ 2 internal holes and skewness k exists if and only if 0 ≤ k ≤ 2m − 2, thus settling in affirmative two conjectures raised in a recent paper by Karimi et al.