Abstract
The paper attempts to classify 5-regular graphs according to their crossing numbers and with given number of vertices. In particular, it is shown that there exist no 5-regular graphs on 12 vertices with crossing number one. This together with a result in [2] imply that the minimum number of vertices in a 5-regular graph with girth three and crossing number one is 14.
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References
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© 2002 Springer-Verlag Berlin Heidelberg
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Chia, G.L., Gan, C.S. (2002). On Crossing Numbers of 5-Regular Graphs. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_26
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DOI: https://doi.org/10.1007/3-540-45655-4_26
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