Linkless embedding (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Linkless embedding" in English language version.

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Robertson, Seymour & Thomas (1993b). Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993b), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society, 28 (1): 84–89, arXiv:math/9301216, doi:10.1090/S0273-0979-1993-00335-5, MR 1164063.
As previously announced by Robertson, Seymour & Thomas (1993b). Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993b), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society, 28 (1): 84–89, arXiv:math/9301216, doi:10.1090/S0273-0979-1993-00335-5, MR 1164063.

arxiv.org

Robertson, Seymour & Thomas (1993b). Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993b), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society, 28 (1): 84–89, arXiv:math/9301216, doi:10.1090/S0273-0979-1993-00335-5, MR 1164063.
Hass, Lagarias & Pippenger (1999). Hass, Joel; Lagarias, Jeffrey C.; Pippenger, Nicholas (1999), "The computational complexity of knot and link problems", Journal of the ACM, 46 (2): 185–211, arXiv:math/9807016, doi:10.1145/301970.301971.
Nešetřil & Thomas (1985); Fleming & Diesl (2005). Nešetřil, Jaroslav; Thomas, Robin (1985), "A note on spatial representation of graphs", Commentationes Mathematicae Universitatis Carolinae, 26 (4): 655–659, archived from the original on 2011-07-18. Fleming, Thomas; Diesl, Alexander (2005), "Intrinsically linked graphs and even linking number", Algebraic & Geometric Topology, 5 (4): 1419–1432, arXiv:math/0511133, doi:10.2140/agt.2005.5.1419.
Flapan et al. (2006) Flapan, Erica; Howards, Hugh; Lawrence, Don; Mellor, Blake (2006), "Intrinsic linking and knotting of graphs in arbitrary 3–manifolds", Algebraic & Geometric Topology, 6 (3): 1025–1035, arXiv:math/0508004, doi:10.2140/agt.2006.6.1025.
As previously announced by Robertson, Seymour & Thomas (1993b). Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993b), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society, 28 (1): 84–89, arXiv:math/9301216, doi:10.1090/S0273-0979-1993-00335-5, MR 1164063.

dml.cz

dspace.dml.cz

Nešetřil & Thomas (1985) Nešetřil, Jaroslav; Thomas, Robin (1985), "A note on spatial representation of graphs", Commentationes Mathematicae Universitatis Carolinae, 26 (4): 655–659, archived from the original on 2011-07-18.
Nešetřil & Thomas (1985); Fleming & Diesl (2005). Nešetřil, Jaroslav; Thomas, Robin (1985), "A note on spatial representation of graphs", Commentationes Mathematicae Universitatis Carolinae, 26 (4): 655–659, archived from the original on 2011-07-18. Fleming, Thomas; Diesl, Alexander (2005), "Intrinsically linked graphs and even linking number", Algebraic & Geometric Topology, 5 (4): 1419–1432, arXiv:math/0511133, doi:10.2140/agt.2005.5.1419.

doi.org

Sachs (1983). Sachs, Horst (1983), "On a spatial analogue of Kuratowski's Theorem on planar graphs – an open problem", in Horowiecki, M.; Kennedy, J. W.; Sysło, M. M. (eds.), Graph Theory: Proceedings of a Conference held in Łagów, Poland, February 10–13, 1981, Lecture Notes in Mathematics, vol. 1018, Springer-Verlag, pp. 230–241, doi:10.1007/BFb0071633, ISBN 978-3-540-12687-4.
Robertson, Seymour & Thomas (1995). Robertson, Neil; Seymour, P. D.; Thomas, Robin (1995), "Sachs' linkless embedding conjecture", Journal of Combinatorial Theory, Series B, 64 (2): 185–227, doi:10.1006/jctb.1995.1032.
Kawarabayashi, Kreutzer & Mohar (2010) Kawarabayashi, Ken-ichi; Kreutzer, Stephan; Mohar, Bojan (2010), "Linkless and flat embeddings in 3-space and the unknot problem", Proc. ACM Symposium on Computational Geometry (SoCG '10), pp. 97–106, doi:10.1145/1810959.1810975, ISBN 978-1-4503-0016-2.
Conway & Gordon (1983); Sachs (1983); Robertson, Seymour & Thomas (1993a). Conway, John H.; Gordon, Cameron McA. (1983), "Knots and links in spatial graphs", Journal of Graph Theory, 7 (4): 445–453, doi:10.1002/jgt.3190070410. Sachs, Horst (1983), "On a spatial analogue of Kuratowski's Theorem on planar graphs – an open problem", in Horowiecki, M.; Kennedy, J. W.; Sysło, M. M. (eds.), Graph Theory: Proceedings of a Conference held in Łagów, Poland, February 10–13, 1981, Lecture Notes in Mathematics, vol. 1018, Springer-Verlag, pp. 230–241, doi:10.1007/BFb0071633, ISBN 978-3-540-12687-4. Robertson, Neil; Seymour, Paul; Thomas, Robin (1993a), "A survey of linkless embeddings", in Robertson, Neil; Seymour, Paul (eds.), Graph Structure Theory: Proc. AMS–IMS–SIAM Joint Summer Research Conference on Graph Minors (PDF), Contemporary Mathematics, vol. 147, American Mathematical Society, pp. 125–136.
Robertson, Seymour & Thomas (1993a). A similar definition of a "good embedding" appears in Motwani, Raghunathan & Saran (1988); see also Saran (1989) and Böhme (1990). Robertson, Neil; Seymour, Paul; Thomas, Robin (1993a), "A survey of linkless embeddings", in Robertson, Neil; Seymour, Paul (eds.), Graph Structure Theory: Proc. AMS–IMS–SIAM Joint Summer Research Conference on Graph Minors (PDF), Contemporary Mathematics, vol. 147, American Mathematical Society, pp. 125–136. Motwani, Rajeev; Raghunathan, Arvind; Saran, Huzur (1988), "Constructive results from graph minors: linkless embeddings", Proc. 29th IEEE Symposium on Foundations of Computer Science (FOCS '88), pp. 398–409, doi:10.1109/SFCS.1988.21956, ISBN 0-8186-0877-3. Saran, Huzur (1989), Constructive Results in Graph Minors: Linkless Embeddings, Ph.D. thesis, University of California, Berkeley.
Robertson, Seymour & Thomas (1993b). Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993b), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society, 28 (1): 84–89, arXiv:math/9301216, doi:10.1090/S0273-0979-1993-00335-5, MR 1164063.
Hass, Lagarias & Pippenger (1999). Hass, Joel; Lagarias, Jeffrey C.; Pippenger, Nicholas (1999), "The computational complexity of knot and link problems", Journal of the ACM, 46 (2): 185–211, arXiv:math/9807016, doi:10.1145/301970.301971.
Conway & Gordon (1983); Foisy (2002). Conway, John H.; Gordon, Cameron McA. (1983), "Knots and links in spatial graphs", Journal of Graph Theory, 7 (4): 445–453, doi:10.1002/jgt.3190070410. Foisy, Joel (2002), "Intrinsically knotted graphs", Journal of Graph Theory, 39 (3): 178–187, doi:10.1002/jgt.10017.
Foisy (2003). Foisy, Joel (2003), "A newly recognized intrinsically knotted graph", Journal of Graph Theory, 43 (3): 199–209, doi:10.1002/jgt.10114.
Nešetřil & Thomas (1985); Fleming & Diesl (2005). Nešetřil, Jaroslav; Thomas, Robin (1985), "A note on spatial representation of graphs", Commentationes Mathematicae Universitatis Carolinae, 26 (4): 655–659, archived from the original on 2011-07-18. Fleming, Thomas; Diesl, Alexander (2005), "Intrinsically linked graphs and even linking number", Algebraic & Geometric Topology, 5 (4): 1419–1432, arXiv:math/0511133, doi:10.2140/agt.2005.5.1419.
Flapan et al. (2006) Flapan, Erica; Howards, Hugh; Lawrence, Don; Mellor, Blake (2006), "Intrinsic linking and knotting of graphs in arbitrary 3–manifolds", Algebraic & Geometric Topology, 6 (3): 1025–1035, arXiv:math/0508004, doi:10.2140/agt.2006.6.1025.
For additional examples of intrinsically triple linked graphs, see Bowlin & Foisy (2004). Bowlin, Garry; Foisy, Joel (2004), "Some new intrinsically 3-linked graphs", Journal of Knot Theory and Its Ramifications, 13 (8): 1021–1028, doi:10.1142/S0218216504003652.
Flapan et al. (2001) Flapan, Erica; Pommersheim, James; Foisy, Joel; Naimi, Ramin (2001), "Intrinsically n-linked graphs", Journal of Knot Theory and Its Ramifications, 10 (8): 1143–1154, doi:10.1142/S0218216501001360.
As previously announced by Robertson, Seymour & Thomas (1993b). Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993b), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society, 28 (1): 84–89, arXiv:math/9301216, doi:10.1090/S0273-0979-1993-00335-5, MR 1164063.
The application of the Robertson–Seymour algorithm to this problem was noted by Fellows & Langston (1988). Fellows, Michael R.; Langston, Michael A. (1988), "Nonconstructive tools for proving polynomial-time decidability", Journal of the ACM, 35 (3): 727–739, doi:10.1145/44483.44491.

gatech.edu

people.math.gatech.edu

Robertson, Seymour & Thomas (1993a). Robertson, Neil; Seymour, Paul; Thomas, Robin (1993a), "A survey of linkless embeddings", in Robertson, Neil; Seymour, Paul (eds.), Graph Structure Theory: Proc. AMS–IMS–SIAM Joint Summer Research Conference on Graph Minors (PDF), Contemporary Mathematics, vol. 147, American Mathematical Society, pp. 125–136.
Conway & Gordon (1983); Sachs (1983); Robertson, Seymour & Thomas (1993a). Conway, John H.; Gordon, Cameron McA. (1983), "Knots and links in spatial graphs", Journal of Graph Theory, 7 (4): 445–453, doi:10.1002/jgt.3190070410. Sachs, Horst (1983), "On a spatial analogue of Kuratowski's Theorem on planar graphs – an open problem", in Horowiecki, M.; Kennedy, J. W.; Sysło, M. M. (eds.), Graph Theory: Proceedings of a Conference held in Łagów, Poland, February 10–13, 1981, Lecture Notes in Mathematics, vol. 1018, Springer-Verlag, pp. 230–241, doi:10.1007/BFb0071633, ISBN 978-3-540-12687-4. Robertson, Neil; Seymour, Paul; Thomas, Robin (1993a), "A survey of linkless embeddings", in Robertson, Neil; Seymour, Paul (eds.), Graph Structure Theory: Proc. AMS–IMS–SIAM Joint Summer Research Conference on Graph Minors (PDF), Contemporary Mathematics, vol. 147, American Mathematical Society, pp. 125–136.
Robertson, Seymour & Thomas (1993a). A similar definition of a "good embedding" appears in Motwani, Raghunathan & Saran (1988); see also Saran (1989) and Böhme (1990). Robertson, Neil; Seymour, Paul; Thomas, Robin (1993a), "A survey of linkless embeddings", in Robertson, Neil; Seymour, Paul (eds.), Graph Structure Theory: Proc. AMS–IMS–SIAM Joint Summer Research Conference on Graph Minors (PDF), Contemporary Mathematics, vol. 147, American Mathematical Society, pp. 125–136. Motwani, Rajeev; Raghunathan, Arvind; Saran, Huzur (1988), "Constructive results from graph minors: linkless embeddings", Proc. 29th IEEE Symposium on Foundations of Computer Science (FOCS '88), pp. 398–409, doi:10.1109/SFCS.1988.21956, ISBN 0-8186-0877-3. Saran, Huzur (1989), Constructive Results in Graph Minors: Linkless Embeddings, Ph.D. thesis, University of California, Berkeley.

utdallas.edu

Truemper (1992). Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101.

web.archive.org

Nešetřil & Thomas (1985) Nešetřil, Jaroslav; Thomas, Robin (1985), "A note on spatial representation of graphs", Commentationes Mathematicae Universitatis Carolinae, 26 (4): 655–659, archived from the original on 2011-07-18.
Nešetřil & Thomas (1985); Fleming & Diesl (2005). Nešetřil, Jaroslav; Thomas, Robin (1985), "A note on spatial representation of graphs", Commentationes Mathematicae Universitatis Carolinae, 26 (4): 655–659, archived from the original on 2011-07-18. Fleming, Thomas; Diesl, Alexander (2005), "Intrinsically linked graphs and even linking number", Algebraic & Geometric Topology, 5 (4): 1419–1432, arXiv:math/0511133, doi:10.2140/agt.2005.5.1419.

zenodo.org

For additional examples of intrinsically triple linked graphs, see Bowlin & Foisy (2004). Bowlin, Garry; Foisy, Joel (2004), "Some new intrinsically 3-linked graphs", Journal of Knot Theory and Its Ramifications, 13 (8): 1021–1028, doi:10.1142/S0218216504003652.