(Preprints)
39. (with Y. Huh) Crossing number of graphs and $\mathsf{\Delta Y}$-move, preprint. (arXiv:math.CO/2402.10633)
38. Converses to generalized Conway-Gordon type congruences, to appear in Tokyo Journal of Mathematics. (arXiv:math.GT/2211.00408)
(Published papers)
37. (with A. Inoue, N. Kimura and K. Taniyama) Crossing numbers and rotation numbers of cycles in a plane immersed graph, J. Knot Theory Ramifications 31 (2022), no. 11, 2250076. (arXiv:math.GT/2205.01013)
36. Capturing links in spatial complete graphs, J. Knot Theory Ramifications 31 (2022), no. 3, 2250022. (arXiv:math.GT/2105.11297)
35. (with H. Morishita) Generalization of the Conway-Gordon theorem and intrinsic linking on complete graphs, Ann. Comb. 25 (2021), 439-470. (arXiv:math.GT/2004.10013)
34. (with E. Flapan and K. Kozai) Stick number of non-paneled knotless spatial graphs, New York J. Math. 26 (2020), 836-852. (arXiv:math.GT/1909.01223)
33. (with H. Morishita) Generalizations of the Conway-Gordon theorems and intrinsic knotting on complete graphs, J. Math. Soc. Japan 71 (2019), no. 4, 1223-1241. (arXiv:math.GT/1807.02805)
32. (with A. Ishii and K. Oshiro) On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links, Osaka J. Math. 55 (2018), no. 2, 297-313. (arXiv:math.GT/1503.07969)
31. (with E. Flapan, T. Mattman, B. Mellor and R. Naimi) Recent developments in spatial graph theory, Knots, Links, Spatial Graphs, and Algebraic Invariants, 81-102, Contemp. Math., 689, Amer. Math. Soc., Providence, RI, 2017. (arXiv:math.GT/1602.08122)
30. $C_{n}$-moves and the difference of Jones polynomials for links, J. Knot Theory Ramifications 26 (2017), no. 5, 1750029.(arXiv:math.GT/1602.02584)
29. (with A. Mizusawa) A homotopy classification of two-component spatial graphs up to neighborhood equivalence, Topology Appl. 196 (2015), Part B, 710-718. (arXiv:math.GT/1212.6629)
28. (with H. Hashimoto) Conway-Gordon type theorem for the complete four-partite graph $K_{3,3,1,1}$, New York J. Math. 20 (2014), 471-495. (arXiv:math.GT/1211.4131)
27. (with E. Flapan and W. Fletcher) Reduced Wu and generalized Simon invariants for spatial graphs, Math. Proc. Cambridge Philos. Soc. 156 (2014), no. 3, 521-544. (arXiv:math.GT/1309.2886)
26. (with H. Hashimoto) On Conway-Gordon type theorems for graphs in the Petersen family, J. Knot Theory Ramifications 22 (2013), no. 9, 1350048. (arXiv:math.GT/1209.2006)
25. (with K. Taniyama) $\triangle Y$-exchanges and the Conway-Gordon theorems, J. Knot Theory Ramifications 21 (2012), no. 7, 1250067. (arXiv:math.GT/1104.0828)
24. (with R. Hanaki, K. Taniyama and A. Yamazaki) On intrinsically knotted or completely 3-linked graphs, Pacific J. Math. 252 (2011), no. 2, 407-425. (arXiv:math.GT/1006.0698)
23. (with Y. Huh) Regular projections of graphs with at most three double points, J. Knot Theory Ramifications 19 (2010), no. 7, 917-933. (arXiv:math.GT/0808.4027)
22. On the Wu invariants for immersions of a graph into the plane, Homology, Homotopy Appl. 12 (2010), no. 1, 45-60. (arXiv:math.GT/0908.3109)
21. Homotopy on spatial graphs and generalized Sato-Levine invariants, Rev. Mat. Complut. 23 (2010), no. 1, 1-17. (arXiv:math.GT/0710.3627)
20. (with K. Taniyama) Symmetries of spatial graphs and Simon invariants, Fund. Math. 205 (2009), no. 3, 219-236. (arXiv:math.GT/0708.0066)
19. A refinement of the Conway-Gordon theorems, Topology Appl. 156 (2009), no. 17, 2782-2794. (arXiv:math.GT/0907.0152)
18. An intrinsic nontriviality of graphs, Algebr. Geom. Topol. 9 (2009), no. 1, 351-364. (arXiv:math.GT/0804.4229)
17. (with T. Fleming) Homotopy on spatial graphs and the Sato-Levine invariant, Trans. Amer. Math. Soc. 361 (2009), no. 4, 1885-1902. (arXiv:math.GT/0509003)
16. Delta edge-homotopy invariants of spatial graphs via disk-summing the constituent knots, Illinois J. Math. 52 (2008), no. 2, 629-644. (arXiv:math.GT/0703319)
15. Achirality of spatial graphs and the Simon invariant, Intelligence of Low Dimensional Topology 2006 (Hiroshima), 239-243, Ser. Knots Everything, 40, World Sci. Publ., 2007. (PDF)
14. An unknotting theorem for delta and sharp edge-homotopy, Math. Nachr. 280 (2007), no. 8, 897--906. (PDF)
13. Regular projections of spatial graphs, Knot Theory for Scientific Objects, Osaka City Advanced Mathematics Institute Studies 1 no. 1, 111-128, Osaka Municipal Universities Press, 2007.
12. Completely distinguishable projections of spatial graphs, J. Knot Theory Ramifications 15 (2006), no. 1, 11-19. (PDF)
11. A remark on the identifiable projections of planar graphs, Kobe J. Math. 22 (2005), no. 1-2, 65-70. (PDF)
10. (with M. Ozawa, K. Taniyama and Y. Tsutsumi) Newly found forbidden graphs for trivializability, J. Knot Theory Ramifications 14 (2005), no. 4, 523-538. (PDF)
9. (with R. Shinjo) On boundary spatial embeddings of a graph, Q. J. Math. 56 (2005), no. 2, 239-249. (PDF)
8. Sharp edge-homotopy on spatial graphs, Rev. Mat. Complut. 18 (2005), no. 1, 181-207.
7. Delta edge-homotopy on theta curves, Math. Proc. Cambridge Philos. Soc. 138 (2005), no. 3, 401-420.
6. (with T. Kanenobu) Delta move and polynomial invariants of links, Topology Appl. 146/147 (2005), 91-104.
5. Edge-homotopy classification of spatial complete graphs on four vertices, J. Knot Theory Ramifications 13 (2004), no. 6, 763-777.
4. (with K. Onda) A characterization of knots in a spatial graph II, J. Knot Theory Ramifications 11 (2002), no. 7, 1133-1154.
3. Delta link-homotopy on spatial graphs, Rev. Mat. Complut. 15 (2002), no. 2, 543-570.
2. Clasp-pass moves on spatial graphs , Interdiscip. Inform. Sci. 7 (2001), no. 1, 113-121.
1. The second skew-symmetric cohomology group and spatial embeddings of graphs, J. Knot Theory Ramifications 9 (2000), no. 3, 387-411.
My Erdos number is less than or equal to 4.
R. Nikkuni - M. Ozawa - J. H. Rubinstein - N. C. Wormald - P. Erdos
R. Nikkuni - T. W. Mattman - J. McKay - J. H. Conway - P. Erdos