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Abstract: Eliahou \cite{2} and Kryuchkov \cite{9} conjectured a proposition thatGravier and Payan \cite{4} proved to be equivalent to the Four Color Theorem.It states that any triangulation of a polygon can be transformed into anothertriangulation of the same polygon by a sequence of signed diagonal flips. It iswell known that any pair of polygonal triangulations are connected by asequence of non-signed diagonal flips. In this paper we give a sufficient andnecessary condition for a diagonal flip sequence to be a signed diagonal flipsequence.



Author: Rui Pedro Carpentier

Source: https://arxiv.org/



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