Tight quadrangulations on the sphere
暂无分享,去创建一个
A quadrangulation is a simple graph on the sphere each of whose faces is quadrilateral. A quadrangulation G is said to be tight if each edge of G is incident to a vertex of degree exactly 3. We prove that any two tight quadrangulations with n>=11 vertices, not isomorphic to pseudo double wheels, can be transformed into each other, through only tight quadrangulations, by at most 83n-763 rhombus rotations. If we restrict quadrangulations to be 3-connected, then the number of rhombus rotations can be decreased to 2n-22.
[1] Atsuhiro Nakamoto. Diagonal transformations in quadrangulations of surfaces , 1996, J. Graph Theory.
[2] Atsuhiro Nakamoto,et al. Diagonal Flips in Hamiltonian Triangulations on the Sphere , 2003, Graphs Comb..
[3] Dan Archdeacon,et al. The construction and classification of self-dual spherical polyhedra , 1992, J. Comb. Theory, Ser. B.
[4] Atsuhiro Nakamoto. Generating quadrangulations of surfaces with minimum degree at least 3 , 1999, J. Graph Theory.