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.
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Karimi S., Lewinter M., Kalyanswamy S. (2007). J. Math. Chem. 37: 59–61
Došlić T. (2007). J. Math. Chem. 41: 217–229
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Došlić, T. On the existence of multiply connected monolayered cyclofusenes with given parameters. J Math Chem 43, 1422–1428 (2008). https://doi.org/10.1007/s10910-007-9265-3
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DOI: https://doi.org/10.1007/s10910-007-9265-3