Algebraic & Geometric Topology Volume 9, issue 1 (2009)

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An intrinsic nontriviality of graphs

Ryo Nikkuni

Algebraic & Geometric Topology 9 (2009) 351–364

DOI: 10.2140/agt.2009.9.351

Bibliography

1	G Bowlin, J Foisy, Some new intrinsically $3$–linked graphs, J. Knot Theory Ramifications 13 (2004) 1021 MR2108646
2	J H Conway, C M Gordon, Knots and links in spatial graphs, J. Graph Theory 7 (1983) 445 MR722061
3	E Flapan, R Naimi, J Pommersheim, Intrinsically triple linked complete graphs, Topology Appl. 115 (2001) 239 MR1847466
4	E Flapan, J Pommersheim, J Foisy, R Naimi, Intrinsically $n$–linked graphs, J. Knot Theory Ramifications 10 (2001) 1143 MR1871222
5	J Foisy, Graphs with a knot or $3$–component link in every spatial embedding, J. Knot Theory Ramifications 15 (2006) 1113 MR2287434
6	L H Kauffman, Formal knot theory, Math. Notes 30, Princeton Univ. Press (1983) MR712133
7	L H Kauffman, On knots, Annals of Math. Studies 115, Princeton Univ. Press (1987) MR907872
8	S V Matveev, Generalized surgeries of three-dimensional manifolds and representations of homology spheres, Mat. Zametki 42 (1987) 268, 345 MR915115
9	T Motohashi, K Taniyama, Delta unknotting operation and vertex homotopy of graphs in $\mathbf R^3$, from: "KNOTS '96 (Tokyo)" (editor S Suzuki), World Sci. Publ. (1997) 185 MR1664961
10	H Murakami, Y Nakanishi, On a certain move generating link-homology, Math. Ann. 284 (1989) 75 MR995383
11	R Nikkuni, Delta edge-homotopy invariants of spatial graphs via disk-summing the constituent knots, to appear in Illinois J. Math. arXiv:math.GT/0703319
12	Y Ohyama, T Tsukamoto, On Habiro's $C_n$–moves and Vassiliev invariants of order $n$, J. Knot Theory Ramifications 8 (1999) 15 MR1673893
13	M Okada, Delta-unknotting operation and the second coefficient of the Conway polynomial, J. Math. Soc. Japan 42 (1990) 713 MR1069853
14	N Robertson, P Seymour, R Thomas, Sachs' linkless embedding conjecture, J. Combin. Theory Ser. B 64 (1995) 185 MR1339849
15	H Sachs, On spatial representations of finite graphs, from: "Finite and infinite sets, Vol. I, II (Eger, 1981)" (editors A Hajnal, L Lovász, V T Sòs), Colloq. Math. Soc. János Bolyai 37, North-Holland (1984) 649 MR818267
16	M Scharlemann, A Thompson, Detecting unknotted graphs in $3$–space, J. Differential Geom. 34 (1991) 539 MR1131443
17	T Soma, H Sugai, A Yasuhara, Disk/band surfaces of spatial graphs, Tokyo J. Math. 20 (1997) 1 MR1451853
18	K Taniyama, Cobordism, homotopy and homology of graphs in $\mathbf{R}^3$, Topology 33 (1994) 509 MR1286929
19	K Taniyama, A Yasuhara, Realization of knots and links in a spatial graph, Topology Appl. 112 (2001) 87 MR1815273
20	Y Q Wu, On planarity of graphs in $3$–manifolds, Comment. Math. Helv. 67 (1992) 635 MR1185812
21	H Yamada, Delta distance and Vassiliev invariants of knots, J. Knot Theory Ramifications 9 (2000) 967 MR1780599