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Let $G$ be a planar graph with a planar embedding with $f$ faces. The degree of a face $f_i$ is the number $a_i$ of edges that are incident to $f_i$ (counting bridges twice). Assume that the faces $f_1$, . . . , $f_f$ are ordered such that their degrees are non descending. Consider the degreesequence ($a_1$, . . . , $a_f$ ) of the faces.

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  • $\begingroup$ Where is your question...? $\endgroup$ – user37238 Apr 3 '15 at 12:48
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Draw a convex hexagon $ABCDEF$ and two diagonals $AC$ and $DF$. Then you have degreesequence $(3,3,4,6)$. If you draw $AC$ as an arc outside of the heaxagon, you have $(3,3,5,5)$.

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  • $\begingroup$ Hello @HagenvonEitzen!!! Do you maybe know what cooperating topological sortings are? $\endgroup$ – evinda Apr 7 '15 at 20:11
  • $\begingroup$ @evinda Whatever I can imagine they are, I certainly cannot relate that subject to this graph.theoretic question $\endgroup$ – Hagen von Eitzen Apr 7 '15 at 21:21

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