A study on local deformations for graphs on surfaces focusing on algebraic invariants

虽然已有许多关于曲面上三角剖分的对角翻转的结果，但如果我们考虑保持这些图的正则性的偶数三角剖分或四边形剖分的局部变形(在这种情况下应该关注曲面上的图的代数不变量)，就变得困难了。我们考虑了这里的问题，并在这些问题上取得了一些结果。特别地，我们证明了射影平面上的任意两个k-极小四边形可以通过一系列Y-旋转相互转换。

Although there are many results on diagonal flips for triangulations on surfaces, it becomes difficult if we consider a local deformation for even triangulations or quadrangulations which preserves the regularity of those graphs(algebraic invariants for graphs on surfaces should be focused in this case). We considered problems around here and could obtain some results on them. Especially, we proved that any two k-minimal quadrangulations on the projective plane can be transformed into each other by a sequence of Y-rotations.