The Crossing Number of The Hexagonal Graph H3,n

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In [C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 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 m-cycle and an n-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 H3, n, which is a special kind of (3,6)-tilings.

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  • [1] J. Adamsson and R.B. Richter Arrangements circular arrangements and the crossing number of C7 × Cn J. Combin. Theory Ser. B 90 (2004) 21–39. doi:10.1016/j.jctb.2003.05.001

  • [2] L.W. Beineke and R.D. Ringeisen On the crossing numbers of products of cycles and graphs of order four J. Graph Theory 4 (1980) 145–155. doi:10.1002/jgt.3190040203

  • [3] D. Bokal On the crossing numbers of Cartesian products with paths J. Combin. Theory Ser. B 97 (2007) 381–384. doi:10.1016/j.jctb.2006.06.003

  • [4] D. Bokal On the crossing numbers of Cartesian products with trees J. Graph Theory 56 (2007) 287–300. doi:10.1002/jgt.20258

  • [5] J.A. Bondy and U.S.R. Murty Graph Theory (Springer New York 2008).

  • [6] M.R. Garey and D.S. Johnson Crossing number is NP-complete SIAM J. Algebraic Discrete Methods 4 (1983) 312–316. doi:10.1137/0604033

  • [7] M. Klešč R.B. Ritcher and I. Stobert The crossing number of C5 × Cn J. Graph Theory 22 (1996) 239–243. doi:10.1002/(SICI)1097-0118(199607)22:3⟨239::AID-JGT4⟩3.0.CO;2-N

  • [8] D.J. Ma H. Ren and J.J. Lu The crossing number of the circular graph C(2m + 2 m) Discrete Math. 304 (2005) 88–93. doi:10.1016/j.disc.2005.04.018

  • [9] T.H. Pak The crossing number of C(3k + 1; {1 k}) Discrete Math. 307 (2007) 2771–2774. doi:10.1016/j.disc.2007.02.001

  • [10] R.B. Richter and G. Salazar The crossing number of C6×Cn Australas. J. Combin. 23 (2001) 135–143.

  • [11] R.B. Richter and J. Širáň The crossing number of K3n in a surface J. Graph Theory 21 (1996) 51–54. doi:10.1002/(SICI)1097-0118(199601)21:1⟨51::AID-JGT7⟩3.0.CO;2-L

  • [12] R.D. Ringeisen and L.W. Beineke The crossing number of C3 × Cn J. Combin. Theory Ser. B 24 (1978) 134–136. doi:10.1016/0095-8956(78)90014-X

  • [13] C. Thomassen Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface Trans. Amer. Math. Soc. 323 (1991) 605–635. doi:10.1090/S0002-9947-1991-1040045-3

  • [14] Y.S. Yang X.H. Lin J.G. Lu and X. Hao The crossing number of C(n; {1 3}) Discrete Math. 289 (2004) 107–118. doi:10.1016/j.disc.2004.08.014

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Target audience:

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

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