The Crossing Number of The Hexagonal Graph H3,n

In [C. Thomassen, , Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus and the Klein bottle into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings. Many authors made great efforts to investigate the crossing number (in the...

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Published inDiscussiones Mathematicae. Graph Theory Vol. 39; no. 2; pp. 547 - 554
Main Authors Wang, Jing, Ouyang, Zhangdong, Huang, Yuanqiu
Format Journal Article
LanguageEnglish
Published Sciendo 01.05.2019
University of Zielona Góra
Subjects
05C10
05C62
Cartesian product
crossing number
hexagonal graph
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Summary:In [C. Thomassen, , Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus and the Klein bottle into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings. Many authors made great efforts to investigate the crossing number (in the plane) of the Cartesian product of an -cycle and an -cycle, which is a special (4,4)-tiling. For other tilings, there are quite rare results concerning on their crossing numbers. This motivates us in the paper to determine the crossing number of a hexagonal graph which is a special kind of (3,6)-tilings.
ISSN:2083-5892
DOI:10.7151/dmgt.2092