Three moves on signed surface triangulations
A finite triangulation of a surface with \(-1\) or \(+1\) assigned to each face has the Heawood property if the sum of the assignments to the faces incident with vertex \(x\) is divisible by \(3\), for every \(x\). The authors introduce three moves on signed surface triangulations that preserve the Heawood property, and they prove that every Heawood signed triangulation of the sphere can be obtained from a Heawood signed triangle, by a sequence of the three moves. Applications are given to 4-vertex-colorings of planar graphs.
scientific article; zbMATH DE number 1843804