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- Dan Archdeacon, Joan Hutchinson, Atsuhiro Nakamoto, Seiya Negami, Katsuhiro Ota
- Journal of Graph Theory
- 2001

It has been shown that every quadrangulation on any nonspherical orientable closed surface with a suf®ciently large representativity has chromatic number at most 3. In this paper, we show that a quadrangulation G on a nonorientable closed surface Nk has chromatic number at least 4 if G has a cycle of odd length which cuts open Nk into an orientable surface.… (More)

- Atsuhiro Nakamoto
- Journal of Graph Theory
- 1996

- Atsuhiro Nakamoto, Katsuhiro Ota
- Journal of Graph Theory
- 1995

- Ryuichi Mori, Atsuhiro Nakamoto, Katsuhiro Ota
- Graphs and Combinatorics
- 2003

In this paper, we shall prove that any two Hamiltonian triangulations on the sphere with n 5 vertices can be transformed into each other by at most 4n 20 diagonal flips, preserving the existence of Hamilton cycles. Moreover, using this result, we shall prove that at most 6n 30 diagonal flips are needed for any two triangulations on the sphere with n… (More)

- Atsuhiro Nakamoto
- J. Comb. Theory, Ser. B
- 1996

A quadrangulation G on a closed surface F 2 is a simple graph embedded in F 2 so that each face of G is quadrilateral. The diagonal slide and the diagonal rotation were defined in [1] as two transformations of quadrangulations. See Fig. 1. We also call the both transformations diagonal transformations in total. If the graph obtained by a diagonal slide is… (More)

- Atsuhiro Nakamoto, Katsuhiro Ota
- J. Comb. Theory, Ser. B
- 1997

- Hideo Komuro, Atsuhiro Nakamoto, Seiya Negami
- J. Comb. Theory, Ser. B
- 1999

- Richard Brunet, Atsuhiro Nakamoto, Seiya Negami
- J. Comb. Theory, Ser. B
- 1996

Consider a class P of triangulations on a closed surface F , closed under vertex splitting. We shall show that any two triangulations with the same and sufficiently large number of vertices which belong to P can be transformed into each other, up to homeomorphism, by a finite sequence of diagonal flips through P. Moreover, if P is closed under… (More)

- Ken-ichi Kawarabayashi, Atsuhiro Nakamoto, Katsuhiro Ota
- J. Comb. Theory, Ser. B
- 2003

- Atsuhiro Nakamoto, Katsuhiro Ota
- J. Comb. Theory, Ser. B
- 1997