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Article Dans Une Revue Graphs and Combinatorics Année : 2016

Some Triangulated Surfaces without Balanced Splitting


Let G be the graph of a triangulated surface Σ of genus g≥2. A cycle of G is splitting if it cuts Σ into two components, neither of which is homeomorphic to a disk. A splitting cycle has type k if the corresponding components have genera k and g−k. It was conjectured that G contains a splitting cycle (Barnette 1982). We confirm this conjecture for an infinite family of triangulations by complete graphs but give counter-examples to a stronger conjecture (Mohar and Thomassen in Graphs on surfaces. Johns Hopkins studies in the mathematical sciences. Johns Hopkins University Press, Baltimore, 2001) claiming that G should contain splitting cycles of every possible type.

Dates et versions

hal-01705333 , version 1 (09-02-2018)



Vincent Despré, Francis Lazarus. Some Triangulated Surfaces without Balanced Splitting. Graphs and Combinatorics, 2016, 32 (6), pp.2339-2353. ⟨10.1007/s00373-016-1735-6⟩. ⟨hal-01705333⟩
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