[HTML][HTML] Tight quadrangulations on the sphere
H Komuro, K Ando, A Nakamoto - Discrete mathematics, 2006 - Elsevier
H Komuro, K Ando, A Nakamoto
Discrete mathematics, 2006•ElsevierA 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.
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.
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.
Elsevier
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