Abstract
Motivated by the connection with the genus of the corresponding link and its application on DNA polyhedral links, in this paper, we introduce a parameter smax(G), which is the maximum number of circles of states of the link diagram D(G) corresponding to a plane (positive) graph G. We show that smax(G) does not depend on the embedding of G and if G is a 4-edge-connected plane graph then smax(G) is equal to the number of faces of G, which cover the results of S. Y. Liu and H. P. Zhang as special cases.
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We thank Professor Hongliang Lu and Dr. Weiling Yang for some helpful discussions.
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This paper is supported by the National Natural Science Foundation of China (Nos 11271307, 11171279 and 11101174).
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Jin, Xa., Ge, J., Cheng, XS. et al. The Number of Circles of a Maximum State of a Plane Graph with Applications. Acta Math. Appl. Sin. Engl. Ser. 37, 409–420 (2021). https://doi.org/10.1007/s10255-021-1020-1
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DOI: https://doi.org/10.1007/s10255-021-1020-1