A simple quadrangulation of the sphere is a finite simple graph embedded on the sphere
such that every face is bounded by a walk of 4 edges. We consider the following classes of …

Note on irreducible triangulations of surfaces Page 1 Note on Irreducible Triangulations of
Atsuhiro Nakamoto Katsuhiro Ota Surf aces DEPARTMENT O f MA TH €MA TICS FACULTY …

DIAGONAL FLIPS OF TRIANGULATIONS Page 1 YOKOHAMA MATHEMATICAL JOURNAL
VOL. 47, 1999 SPECIAL ISSUE DIAGONAL FLIPS OF TRIANGULATIONS ON SURFACES …

THE DIAGONAL FLIPS OF TRIANGULATIONS ON THE SPHERE Page 1 YOKOHAMA
MATHEMATICAL JOURNAL VOL. 44, 1997 THE DIAGONAL FLIPS OF TRIANGULATIONS ON …

It has been shown that every quadrangulation on any nonspherical orientable closed
surface with a sufficiently large representativity has chromatic number at most 3. In this …

In this article, we show that all quadrangulations of the sphere with minimum degree at least
3 can be constructed from the pseudo‐double wheels, preserving the minimum degree at …

A diagonal flip is an operation that converts one triangulation of a convex polygon into
another. In this paper we generalize this operation to prove some results including the next …

Consider a class P of triangulations on a closed surfaceF2, closed under vertex splitting. We
shall show that any two triangulations with the same and sufficiently large number of vertices …

The first paper of this series of articles revealed that Four-Color Conjecture is hopefully
proved mathematically by investigating a special class of graphs, called the 4-chromatic …

In this paper, we find the irreducible quadrangulations of the torus. As a consequence, any
two quadrangulations of the torus with the same number of vertices that are either both …