論文と著書

論文（Papers）と著書（Books）

論文（Papers）

1993
1. S. Negami and A. Nakamoto, Diagonal transformations of graphs on closed surfaces, Sci. Rep. Yokohama Nat. Univ., Sec. I No. 40,(1993) 71--97. (Non-Refereed)

1995
2. A. Nakamoto and K. Ota, Note on irreducible triangulations of surfaces, J. Graph Theory 20 (1995), 227--233.
3. A. Nakamoto, Irreducible quadrangulations of the Klein bottle, Yokohama Math. J. 43 (1995), 125--139.

1996
4. A. Nakamoto, Diagonal transformations in quadrangulations of surfaces, J. Graph Theory 21 (1996), 289--299.
5. A. Nakamoto, Irreducible quadrangulations of the torus, J. Combin. Theory, Ser. B 67 (1996), 183--201.
6. A. Nakamoto, Diagonal transformations and cycle parities of quadrangulations on surfaces, J. Combin. Theory, Ser. B 67 (1996), 202--211.
7. R. Brunet, A. Nakamoto and S. Negami, Diagonal flips of triangulations on closed surfaces preserving specified properties, J. Combin. Theory, Ser. B 68 (1996), 295--309.

1997
8. A. Nakamoto, K. Ota and T. Tanuma, Three-cycle reversions in oriented planar triangulations, Yokohama Math. J. 44 (1997), 123--139.
9. A. Nakamoto and K. Ota, Diagonal transformations in quadrangulations and Dehn twists preserving cycle parities, J. Combin. Theory, Ser. B 69 (1997), 125--141.
10. A. Nakamoto and K. Ota, Diagonal transformations of graphs and Dehn twists of surfaces, J. Combin. Theory, Ser. B 70 (1997), 292--300.
11. S. Negami, A. Nakamoto and T. Tanuma, Re-embedding structures of triangulations on closed surfaces, Sci. Rep. Yokohama Nat. Univ., Sec. I No. 44 (1997), 41--55. (Non-Refereed)

1998

1999
12. A. Nakamoto, Transformations in closed 2-cell embeddings on surfaces preserving specified properties, Discrete Math. 197/198 (1999), 607--615.
13. A. Nakamoto, Generating quadrangulations of surfaces with minimum degree at least 3, J. Graph Theory 30 (1999), 223--234.
14. H. Komuro, A. Nakamoto and S. Negami, Diagonal flips in triangulations on closed surfaces with minimum degree at least 4, J. Combin. Theory, Ser. B 76 (1999), 68--92.
15. A. Nakamoto, The Y Δ-equivalence of kernels on the torus without taking duals, Yokohama Math. J. 47 Special Issue (1999), 183--189.
16. R. Brunet, A. Nakamoto and S. Negami, Every 5-connected triangulation of the Klein bottle is Hamiltonian, Yokohama Math. J. 47 Special Issue (1999), 239--244.

2000
17. C. Cortes and A. Nakamoto, Diagonal flips in outer-torus triangulations, Discrete Math. 216 (2000), 71--83.
18. C.Cortes and A. Nakamoto, Diagonal flips in outer-Klein-bottle triangulations, Discrete Math. 222 (2000), 41--50.
19. A. Nakamoto and M. Watanabe, Cycle reversals in orientated plane quadrangulations and orthogonal plane partitions, J. Geometry 68 (2000), 200-- 208.
20. A. Nakamoto and S. Negami, Full-symmetric embeddings of graphs on closed surfaces, Memoirs of Osaka Kyoiku University, Ser III, 49 No.1 (2000), 1--15. (Non-Refereed)
21. D. Archdeacon, J. Hutchinson, A. Nakamoto, S. Negami and K. Ota, Chromatic numbers of quadrangulations on closed surfaces, J. Graph Theory 37 (2001), 100--114.

2001
22. A. Nakamoto and S. Negami, Note on diagonal flips and chromatic numbers of quadrangulations on closed surfaces, Discrete and Computational Geometry (Lecture Notes in Computer Science 2098, Springer) (2001), 274--279.
23. K. Kawarabayashi, A. Nakamoto, Y. Oda and M. Watanabe, Geometric Transformations in plane triangulations, Discrete and Computational Geometry (Lecture Notes in Computer Science 2098, Springer) (2001), 217--221.
24. A. Nakamoto, Triangle contact systems, orthogonal plane partitions and their hit graphs, Discrete and Computational Geometry (Lecture Notes in Computer Science 2098, Springer) (2001), 264--273.
25. A. Nakamoto, Quadrangulations on closed surfaces, Interdiscip. Inform. Sci. 7 (2001), 77--98.
26. S. Negami and A. Nakamoto, Triangulations on closed surfaces covered by vertices of given degree, Graphs Combin. 17 (2001), 529--537.

2002
27. A. Nakamoto and S. Negami, Generating triangulations of closed surfaces with minimum degree at least 4, Discrete Math. 244 (2002), 345-349.
28. K. Ando and A. Nakamoto, On quadrangulations of closed surfaces covered by vertices of degree 3, Ars Combin. 62 (2002), 121--127.
29. M. Hama and A. Nakamoto, Generating 4-connected triangulations on closed surfaces, Memoirs of Osaka Kyoiku University, Ser III, 50 (2002), 145-153. (Non-Refereed)
30. C. Cortes, C. Glima, A. Marquez and A. Nakamoto, Diagonal flips in outer-triangulations on closed surfaces, Discrete Math. 254 (2002), 63-74.
31. A. Nakamoto and S. Negami, Diagonal flips in graphs on closed surfaces with specified face size distribution, Yokohama Math. J. 49 (2002), 171--180.
32. S. Hara and A. Nakamoto, Achromatic numbers of maximal outerplanar graphs, Yokohama Math. J. 49 (2002), 181--186.
33. K. Kawarabayashi, A. Nakamoto, Y. Oda, K. Ota, S. Tazawa and M. Watanabe, On separable self-complementary graphs, Discrete Math. 257 (2002), 165--167.
34. A. Nakamoto and M. Watanabe, How many tetrahedra?, Math. Gaz. 86 (2002), 491--498.
35. K. Ando and A. Nakamoto, Self-complementary graphs with minimum degree 2, Ars Combin. 65 (2002), 65--74.
36. A. Nakamoto, S. Negami, K. Ota, Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces, Electronic Notes in Discrete Mathematics 11 (2002), 509--518. (Non-Refereed)
37. A. Nakamoto, K. Ota, M. Watanabe, On 3-coloring of plane triangulations, Electronic Notes in Discrete Mathematics 11 (2002), 519-524. (Non-Refereed)

2003
38. K. Kawarabayashi, A. Nakamoto and K. Ota, 2-Connected 7-coverings of 3-connected graphs on surfaces, J. Graph Theory 43 (2003), 26--36.
39. R. Mori, A. Nakamoto and K. Ota, Diagonal flips in Hamiltonian plane triangulations, Graphs Combin. 19 (2003), 413--418.
40. K. Kawarabayashi, A. Nakamoto and K. Ota, Subgraphs of graphs on surfaces with high representativity, J. Combin. Theory, Ser. B 89 (2003), 209--229.

2004
41. A. Nakamoto, Four-regular graphs which quadrangulate both the torus and the Klein bottle, Austlaras. J. Combin. 29 (2004), 249--257.
42. A. Nakamoto, S. Negami and K. Ota, Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces, Discrete Math. 285 (2004), 211--218.
43. A. Nakamoto, S. Negami, K. Ota and J. Siran, Planar triangulations quadrangulating other surfaces, Eulopean. J. Combin. 25 (2004), 817--833.

2005
44. A. Nakamoto, K. Ota and M. Watanabe, On 3-coloring of plane triangulations, Ars Combin. 75 (2005), 157--162.
45. K. Kawarabayashi, A. Nakamoto, Y. Oda and M. Watanabe, Acute triangles of 4-connected plane triangulations, Discrete Math. 292 (2005), 95--106.
46. A. Nakamoto, 5-Chromatic even triangulations on the Klein bottle, Discrete Math. 303 (2005), 154--166.
47. K. Koyama and A. Nakamoto, Acute triangles of plane triangulations with minimum degree at least 4, Discrete Math. 303 (2005), 104--116.
48. R. Mori and A. Nakamoto, Diagonal flips in Hamiltonian triangulations on the projective plane, Discrete Math. 303 (2005), 142--153.

2006
49. A. Nakamoto, T. Sakuma and Y. Suzuki, N-Flips in even triangulations on the sphere, J. Graph Theory 51 (2006), 260--268.
50. K. Ando, H. Komuro and A. Nakamoto, Tight quadrangulations on the sphere, Discrete Math. 360 (2006), 278--283.

2007
51. A. Nakamoto, Y. Oda and K, Ota, K6-Minors in triangulations on the double torus, Congr. Numer. 188 (2007), 150--160.
52. A. Nakamoto and N. Sasanuma, 3-Coloring of even embeddings on surfaces, Graphs Combin. 23 (2007), 87--95.
53. K. Kawarabayashi and A. Nakamoto, The Erdos - Posa Property for vertex- and edge-disjoint odd cycles in graphs on orientable surfaces, Discrete Math. 307 (2007), 764--768.

2008
54. A. Nakamoto, 5-Chromatic even triangulations on surfaces, Discrete Math. 308 (2008), 2571--2580.
55. P.C. Bonnington, A. Nakamoto, Geometric realization of a projective triangulation with one face removed, Discrete Comp. Geom. 40 (2008), 141--157.
56. A. Nakamoto and Y. Suzuki, N-Flips in even triangulations on the projective plane, Discrete Math. 308 (2008), 5454--5462.
57. K. Kawarabayashi, R. Mukae and A. Nakamoto, K6-Minors in triangulations in triangulations on the Klein bottle, SIAM J. Discrete Math. 23 (2008), 96--108.
58. M. Chavez, G. Fijavz, A. Marquez, A. Nakamoto, and E. Suarez, Geometric realization of triangulations on the M\"obius band, SIAM J. Discrete Math. 23 (2008), 221--232.
59. Atsuhiro Nakamoto, Geometric realization of a triangulation on the projective plane with one face removed, Electronic Notes in Discrete Mathematics 31 (2008), 243-246. (Non-Refereed)
60. K. Kawarabayashi, A. Nakamoto, Y. Suzuki, N-Flips in even triangulations on surfaces, Electronic Notes in Discrete Mathematics 31 (2008), 99--104. (Non-Refereed)

2009
61. K. Kawarabayashi, A. Nakamoto and Y. Suzuki, N-Flips in even triangulations on surfaces, J. Combin. Theory, Ser. B. 99 (2009), 229--246.
62. R. Mukae and A. Nakamoto, K6-Minors in triangulations and complete quadrangulations, J. Graph Theory 60 (2009), 302--312.
63. A. Nakamoto, K. Ota and Y. Oda, 3-trees with a few vertices of degree 3 in 3-connected planar graphs, Discrete Math. 309 (2009), 666--672.
64. A. Nakamoto and N. Sasanuma, Chromatic numbers of 6-regular graphs on the Klein bottle, Australas. J. Combin. 45 (2009), 73--85.
65. A. Nakamoto, T. Shirakura and S. Tazawa, An alternative enumeration of self-complementary graphs, Util. Math. 80 (2009), 25--32.

2010
66. K. Kawarabayashi, T. Honjo and A. Nakamoto, Dominating sets in triangulations on surfaces, J. Graph Theory 63 (2010), 17--30.
67. A. Nakamoto and Y. Suzuki, Diagonal flips in quadrangulations on the sphere, Yokohama Math. J. 55 (2010), 105--112.
68. R. Mukae, A. Nakamoto, Y. Oda and Y. Suzuki, K6-Minors in triangulations on the nonorientable surface of genus 3, Graphs Combin. 26 (2010), 559--570.

2011
69. Y. Higuchi, A. Nakamoto, K. Ota and T. Sakuma, N-Flips in even triangulations and Dehn twists on the torus, Discrete Math. 311 (2011), 1128--1135. (Non-Refereed)
70. N. Matsumoto, A. Nakamoto, Transformations in hexangulations on the sphere, Electronic Notes in Discrete Mathematics 38 (2011), 621-626.

2012
71. A. Nakamoto and K. Ozeki, Hamiltonian cycles in bipartite quadrangulations on the torus, J. Graph Theory 69 (2012), 143--151.
72. A. Nakamoto and S. Tsuchiya, A face of a projective triangulation removed for its geometric realizability, Discrete Comp. Geom. 47 (2012), 215--234.
73. E. Horev, M.J. Katz, R. Krakovski and A. Nakamoto, Polychromatic 4-coloring of cubic bipartite plane graphs, Discrete Math. 312 (2012), 715--719.
74. A. Nakamoto and Y. Suzuki, Y-Rotations in k-minimal quadrangulations on the projective plane, J. Graph Theory 69 (2012), 301--313.
75. A. Nakamoto and S. Tsuchiya, On geometrically realizable M\"obius triangulations, Discrete Math. 312 (2012), 2135--2139.
76. A. Nakamoto, K. Ota and K. Ozeki, Book embedding of toroidal bipartite graphs, SIAM J. Discrete Math. 26 (2012), 661--669.
77. D. Kral', B. Mohar, A. Nakamoto, O. Pangrac and Y. Suzuki, Coloring Eulerian triangulations of the Klein bottle, Graphs Combin. 28 (2012), 499--530.
78. J. Caceres, C. Cortes, C. Grima, M. Hachimori, A. Marquez, R. Mukae, A. Nakamoto, S. Negami, R. Robles, J. Valenzuela, Compact Grid Representation of Graphs, Lecture Notes in Computer Science 7579 (2012), ISBN 978-3-642-34190-8, 166--174.

2013
79. J. Fujisawa, A. Nakamoto and K. Ozeki, Hamiltonian cycles in bipartite toroidal graphs with a partite set of degree four vertices, J. Combin. Theory, Ser. B 113 (2013), 46--60.
80. A. Nakamoto and S. Tsuchiya, HISTs in triangulations on surfaces, AKCE Int. J. Graphs Combin. 10 (2013), 1--14.
81. M. Kobayashi, A. Nakamoto and T. Yamaguchi, Polychromatic 4-coloring of cubic even embeddings on the projective plane, Discrete Math. 313 (2013), 2423--2431. DOI 10.1016/j.disc.2013.07.005.33
82. V. Alvarez and A. Nakamoto, Colored quadrangulation with Steiner points, LNCS 8296, Springer (J. Akiyama, M. Kano, and T. Sakai (Eds.): TJJCCGG 2012), 20--29, 2013.
83. N. Matsumoto and A. Nakamoto, The number of diagonal transformations in quadrangulations on the sphere, LNCS 8296, Springer (J. Akiyama, M. Kano, and T. Sakai (Eds.): TJJCCGG 2012), 110--119, 2013.
84. A. Boulch, E. Colin de Verdiere and A. Nakamoto, Irreducible triangulations of surfaces with boundary, Graphs Combin. 29 (2013), 1675--1688. DOI 10.1007/s00373-012-1244-1.
85. 中本敦浩，曲面上のグラフの多色彩色について (デザイン、符号、グラフおよびその周辺)，数理解析研究所講究録 (2013), 1844: 146-152，http://hdl.handle.net/2433/195020

2014
86. S. Kato, R. Mori and A. Nakamoto, Quadrangulations on 3-colored point sets with Steiner points and their winding number, Graphs Combin. 30 (2014), 1193--1205. DOI 10.1007/s00373-013-1346-4.
87. M. Nagashima, A. Nakamoto and S. Negami, Generating 3-connected quadrangulations on surfaces, Ars Combin. 116 (2014), 371-384.
88. R. Mukae, A. Nakamoto and Y. Suzuki, 3-Polychromatic quadrangulations on surfaces, Congr. Numer. 219 (2014), 43--51.

2015
89. N. Matsumoto and A. Nakamoto, Generating 4-connected even triangulations on the sphere, Discrete Math. 338 (2015), 64--70. DOI 10.1016/j.disc.2014.08.017
90. S. Bau, N. Matsumoto, A. Nakamoto, L. Zheng, Minor relation for quadrangulations on the sphere, Graphs Combin. 31(2015), 2029--2036. DOI 10.1007/s00373-014-1489-y
91. Y. Kawasaki, N. Matsumoto, A. Nakamoto, N-flips in 4-connected even triangulations on the sphere, Graphs Combin. 31 (2015), 1889--1904. DOI 10.1007/s00373-015-1574-x
92. A. Nakamoto, K. Noguchi and K. Ozeki, Extension to even triangulations on surfaces, SIAM J. Discrete Math. 29 (2015), 2075--2081. DOI:10.1137/140963340
93. A. Nakamoto and T. Nozawa, Book embedding of projective-planar graphs, Congr. Numer. 225 (2015), 63--71.

2016
94. A. Nakamoto, K. Noguchi and K. Ozeki, Cyclic 4-coloring of graphs on surfaces, J. Graph Theory 82 (2016), 265--278. DOI 10.1002/jgt.21900
95. N. Matsumoto, A. Nakamoto and S. Yonekura, Minor relation for quadrangulations on the projective plane, Discrete Applied Math. 209 (2016), 296--302. doi:10.1016/j.dam.2015.07.037
96. G. Fijavz and A. Nakamoto, Odd complete minors in even embeddings on surfaces, Discrete Math. 239 (2016), 165--178. 10.1016/j.disc.2015.07.015
97. A. Nakamoto and T. Nozawa, Book embedding of orientable locally planar graphs, Discrete Math. 339 (2016), 2672--2679. 10.1016/j.disc.2016.05.006
98. M. Kasai, N. Matsumoto, A. Nakamoto, Gr\"unbaum coloring of triangulations on the projective plane, Discrete Applied Math. 215 (2016), 155--163. http://dx.doi.org/10.1016/j.dam.2016.07.012
99. A. Nakamoto, S. Negami, K. Ohba, Y. Suzuki, Looseness and independence number of triangulations on closed surfaces, Discuss. Math. Graph Theory 36 (2016), 545--554. DOI: 10.7151/dmgt.1870

2017
100. A. Nakamoto and K. Ozeki, Coloring of locally planar graphs on surfaces with one color class small, Australasian J. Comb. 67 (2017), 101--108.
101. M. Kasai, N. Matsumoto, A. Nakamoto, T. Nozawa, Y. Takiguchi, H. Seno, Note On 6-regular Graphs on the Klein Bottle, Theory and Applications of Graphs, Vol. 4 (Issue 1) (2017), Article 5. http://digitalcommons.georgiasouthern.edu/tag/vol4/iss1/5
102. Y. Kawasaki and A. Nakamoto, N-flips in even triangulations on the projective plane preserving chromatic number, Yokohama Math. J. 63 (2017), 75--89.
103. N. Matsumoto, A. Nakamoto and S. Yonekura, Quadrangulations on the projective plane with a $K_{3,4}$-minor, Yokohama Math. J. 63 (2017), 117—129.

2018
104. M. Kotrbcik, B Mohar, N. Matsumoto, A. Nakamoto, K. Noguchi, K. Ozeki and A. Vodopivec, Gr\"unbaum coloring of Eulerian triangulations on surfaces, J. Graph Theory 87 (2018), 475--491. DOI: 10.1002/jgt.22169
105. A. Nakamoto, Y. Oda, T. Yamashita and M. Watanabe, A note on two geometric paths with few crossings for points labeled by integers in the plane, Discrete Math. 341 (2018), 1109—1113. DOI 10.1016/j.disc.2017.10.021
106. N. Matsumoto, A. Nakamoto, T. Yamaguchi, Generating even triangulations on the torus, Discrete Math. 341 (2018), 2035—2048. doi.org/10.1016/j.disc.2018.04.002
107. Y. Asayama, N. Matsumoto and A. Nakamoto, S. Ogano, Generating even triangulations on the Klein bottle, Graphs Combin. 34 (2018), 727--757. doi.org/10.1007/s00373-018-1909-5
108. Y. Asayama, Y. Kawasaki, S-J, Kim, A. Nakamoto, and K. Ozeki, 3-dynamic coloring of planar triangulations, Discrete Math. 341 (2018), 2988--2994. doi.org/10.1016/j.disc.2018.07.020
109. A. Nakamoto, G. Kawatani, N. Matsumoto, J. Urrutia, Geometric quadrangulations of a polygon, Electronic Notes in Discrete Mathematics 68 (2018), 59--64. (Non-Refereed)

2019
110. A. Nakamoto, K. Noguchi and K. Ozeki, Spanning bipartite quadrangulations of even triangulations, J. Graph Theory 90 (2019), 267—287. doi.org/10.1002/jgt.22400
111. A. Nakamoto, K. Noguchi and K. Ozeki, Extension to 3-colorable triangulations on surfaces, SIAM J. Discrete Math. 33(3), 1390--1414. doi.org/10.1137/17M1135505
112. K. Ozeki, A. Nakamoto and T. Nozawa, Book embedding of graphs on the projective plane, SIAM J. Discrete Math. 33(4), 1801--1836. doi.org/10.1137/16M1076174

2020
113. N. Matsumoto, A. Nakamoto and S. Negami, Diagonal flips in plane graphs with triangular and quadrangular faces, Discrete Appl. Math. 283 (2020), 292--305. doi.org/10.1016/j.dam.2020.01.007
114. Y. Asayama, R. Matsukawa, N. Matsumoto and A. Nakamoto, $N$-flips in triangulations with two odd degree vertices, Graphs Combin. 36 (2020), 469--490. doi.org/10.1007/s00373-019-02130-2
115. H. Hamanaka, A. Nakamoto and Y. Suzuki, Rhombus tilings of an even-sided polygon and quadrangulations on the projective plane, Graphs Combin. 36 (2020), 561--571. doi.org/10.1007/s00373-020-02137-0

2021
116. A. Nakamoto and Y. Omizo, Y-equivalence and rhombic realization of projective-planar quadrangulations, Discrete Appl. Math. 299 (2021), 98--112. doi.org/10.1016/j.dam.2021.04.026
117. 中本敦浩，小関健太，四足定理とその後，「数学」73(2) （2021年4月) 岩波書店, 133--160.
118. F. Hidaka, N. Matsumoto and A. Nakamoto, Quadrangulations of a polygon with spirality, Graphs Combin. 37 (2021), 1905--1912. doi.org/10.1007/s00373-021-02346-1

2022
119. D. Ikegami and A. Nakamoto, Flippable edges in triangulations on surfaces, Discuss. Math. Graph Theory 2 (2022) 1041--1059. https://doi.org/10.7151/dmgt.2377

2023
None

2024
120. A. Nakamoto and Y. Suzuki, Partially broken orientations of Eulerian graphs on closed surfaces, Discrete Math. 347 (2024), 114016. doi.org/10.1016/j.disc.2024.114016
121. A. Nakamoto, K. Ozeki and D. Takahashi, 2-Connected spanning subgraphs of circuit graphs, to appear in Discrete Math.

2024+
122. A. Nakamoto, Diagonal flips in triangulations on closed surfaces, a survey, Yokohama Math. J., to appear.
123. Y. Kawasaki, N. Matsumoto and A. Nakamoto, Linear number of diagonal flips in 4-connected triangulations on the sphere, submitted.
124. M. Hachimori, A. Nakamoto and K. Ozeki, Coloring zonotopal quadrangulations of the projective space, submitted.
125. A. Nakamoto and D. Takahashi, Quadrangulations of a polygon with a fixed spirality using Steiner points, submitted.
126. T. Kaneko and A. Nakamoto, Orthogonal annulus partitions and their representation, submitted.

数学教育についての論文（Papers on Mathematical Education）

1. 柳本朋子・中本敦浩・桝田尚之，「グラフ理論の教材化について—中学生を対象として—」，大阪教育大学紀要，第III部門，第50巻，第2号，201--212，2002.
2. 柳本朋子・中本敦浩・福山志穂，「グラフ理論の教育について—小学生を対象として—」，大阪教育大学紀要，第III部門，第51巻，第1号，89--99，2002.

著書（Books）

1. 基礎数学力トレーニング，根上生也著，日本評論社，2003年.
2. 離散数学への招待（上下），J.マトウシェック，J. ネシェトリル著，根上生也，中本敦浩訳，シュプリンガーフェアラーク東京，2003年.
3. 数学の最先端21世紀への挑戦. v.4，中本敦浩共訳，シュプリンガーフェアラーク東京，2003年.
4. 曲面上のグラフ理論，中本敦浩，小関健太著，サイエンス社，2021年.
5. 新編数学I, 新興出版社啓林館 2022年.
6. 新編数学A, 新興出版社啓林館 2022年.
7. 新編数学II, 新興出版社啓林館 2022年.
8. ガイダンス離散数学，中本敦浩，小関健太著，サイエンス社，2023年.