On signed diagonal flip sequences

Details On signed diagonal flip sequences On signed diagonal flip sequences

2009-06-29

arxiv.org/abs/0906.5319v2

Mathematics

Combinatorics

11 pages, 24 figures, to appear in European Journal of Combinatorics

Scientific paper

Eliahou \cite{2} and Kryuchkov \cite{9} conjectured a proposition that Gravier 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 another triangulation of the same polygon by a sequence of signed diagonal flips. It is well known that any pair of polygonal triangulations are connected by a sequence of (non-signed) diagonal flips. In this paper we give a sufficient and necessary condition for a diagonal flip sequence to be a signed diagonal flip sequence.

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