A theorem on graph embedding with a relation to hyperbolic volume

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• 作者：Alexander Stoimenow
• 关键词：Mathematics Subject Classiffication (2000)05C10 ; 57Q15 ; 57M25 ; 57M50
• 刊名：Combinatorica
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：36
• 期：5
• 页码：557-589
• 全文大小：695 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1439-6912
• 卷排序：36

文摘

We prove that a planar cubic cyclically 4-connected graph of odd χ < 0 is the dual of a 1-vertex triangulation of a closed orientable surface. We explain how this result is related to (and applied to prove at a separate place) a theorem about hyperbolic volume of links: the maximal volume of alternating links of given χ < 0 does not depend on the number of their components.