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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 paper, we show that a… (More)

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

Abstract.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… (More)

- Hikoe Enomoto, Tomoki Nakamigawa, Katsuhiro Ota
- J. Comb. Theory, Ser. B
- 1997

The pagenumberp(G) of a graphGis defined as the smallestnsuch thatGcan be embedded in a book withnpages. We give an upper bound for the page-number of the complete bipartite graphKm,n. Among other… (More)

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

Let G be a 3-connected graph with n vertices on a non-spherical closed surface Fk2 of Euler genus k with sufficiently large representativity. In this paper, we first study a new cutting method which… (More)

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

In this paper, we shall show that an irreducible triangulation of a closed surface F2 has at most cg vertices, where g stands for a genus of F2 and c a constant. © 1995, John Wiley & Sons, Inc.

- Katsuhiro Ota
- Discrete Mathematics
- 1995

Abstract Let S be a set of vertices of a k -connected graph G . We denote the smallest sum of degrees of k + 1 independent vertices of S by σ k + 1 ( S ; G ). We obtain a sharp lower bound of σ k + 1… (More)

- Ken-ichi Kawarabayashi, Haruhide Matsuda, Yoshiaki Oda, Katsuhiro Ota
- Journal of Graph Theory
- 2002

- Hikoe Enomoto, Miki Shimabara Miyauchi, Katsuhiro Ota
- Discrete Applied Mathematics
- 1999

Abstract In a topological book embedding of a graph, the graph is drawn in a topological book by placing the vertices along the spine of the book and drawing the edges in the pages; edges are allowed… (More)

- Peter Frankl, Katsuhiro Ota, Norihide Tokushige
- J. Comb. Theory, Ser. A
- 1996

We discuss the maximum size of uniform intersecting families with covering number at least?. Among others, we construct a largek-uniform intersecting family with covering numberk, which provides a… (More)

- Atsuhiro Nakamoto, Yoshiaki Oda, Katsuhiro Ota
- Discrete Mathematics
- 2009

A circuit graph(G,C) is a 2-connected plane graph G with an outer cycle C such that from each inner vertex v, there are three disjoint paths to C. In this paper, we shall show that a circuit graph… (More)