|
Linkless embeddings of graphs in $3$-space
Author(s):
Neil
Robertson;
P.
D.
Seymour;
Robin
Thomas
Journal:
Bull. Amer. Math. Soc.
28
(1993),
84-89.
MSC (1991):
Primary 05C10, 05C75, 57M05, 57M15, 57M25
MathSciNet review:
1164063
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [1]
- T. B\"ohme, On spatial representations of graphs, Contemporary Methods in Graph Theory (R. Bodendieck, ed.), Mannheim, Wien, Zurich, 1990, pp.~151--167. MR 1126225
- [2]
- T. B\"ohme, Lecture at the AMS Summer Research Conference on Graph Minors, Seattle, WA, June 1991. MR
- [3]
- J. H. Conway and C. McA. Gordon, Knots and links in spatial graphs, J. Graph Theory \textbf{7} (1983), 445--453. MR 722061
- [4]
- G. M. Fisher, On the group of all homeomorphisms of a manifold, Trans. Amer. Math. Soc. \textbf{97} (1960), 193--212. MR 117712
- [5]
- D. W. Hall, A note on primitive skew curves, Bull. Amer. Math. Soc. \textbf{49} (1943), 935--937. MR 9442
- [6]
- C. Kuratowski, Sur le probl\`eme des courbes gauches en topologie, Fund. Math. \textbf{15} (1930), 271--283. MR
- [7]
- W. K. Mason, Homeomorphic continuous curves in $2$-space are isotopic in $3$-space, Trans. Amer. Math. Soc. \textbf{142} (1969), 269--290. MR 246276
- [8]
- R. Motwani, A. Raghunathan, and H. Saran, Constructive results from graph minors{\rm :} Linkless embeddings, Proc. 29th Symposium on the Foundations of Computer Science, Yorktown Heights, 1988. MR
- [9]
- N. Robertson and P. D. Seymour, Graph minors. {\rm XIII}. The disjoint paths problem, {\rm submitted}. MR
- [10]
- N. Robertson, P. D. Seymour, and R. Thomas, Kuratowski chains, {\rm submitted}. MR
- [11]
- N. Robertson, P. D. Seymour, and R. Thomas, Petersen family minors, {\rm submitted}. MR
- [12]
- N. Robertson, P. D. Seymour, and R. Thomas, Sachs' linkless embedding conjecture, {\rm manuscript}. MR
- [13]
- H. Sachs, On spatial representation of finite graphs {\rm (Proceedings of a conference held in} {\rm \L ag\'ow, February 10--13, 1981, Poland), Lecture Notes in Math., vol. 1018}, Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1983. MR 730653
- [14]
- H. Sachs, On spatial representations of finite graphs, finite and infinite sets, (A. Hajnal, L. Lov\'asz, and V. T. S\'os, eds), Colloq. Math. Soc. J\'anos Bolyai, vol. 37, North-Holland, Budapest, 1984, pp. 649--662. MR 818267
- [15]
- H. Saran, Constructive results in graph minors{\rm :} Linkless embeddings, Ph.D. thesis, University of California at Berkeley, 1989. MR
- [16]
- M. Scharlemann and A. Thompson, Detecting unknotted graphs in {\rm 3}-space, J. Differential Geom. \textbf{34} (1991), 539--560. MR 1131443
- [17]
- H. Whitney, {\rm 2}-isomorphic graphs, Amer. J. Math. \textbf{55} (1933), 245--254. MR 1506961
- [18]
- Y.-Q. Wu, On planarity of graphs in {\rm 3}-manifolds, Comment. Math. Helv. MR 1185812
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1991):
05C10, 05C75, 57M05, 57M15, 57M25
Retrieve articles in all Journals with MSC
(1991):
05C10, 05C75, 57M05, 57M15, 57M25
Additional Information:
DOI:
10.1090/S0273-0979-1993-00335-5
PII:
S 0273-0979(1993)00335-5
|
