Algebraic & Geometric Topology Volume 7, issue 3 (2007)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Mutant knots and intersection graphs

Sergei V Chmutov and Sergei K Lando

Algebraic & Geometric Topology 7 (2007) 1579–1598

DOI: 10.2140/agt.2007.7.1579

Bibliography

1	D Bar-Natan, The Knot Atlas
2	D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
3	A Bouchet, Reducing prime graphs and recognizing circle graphs, Combinatorica 7 (1987) 243 MR918395
4	A Bouchet, Circle graph obstructions, J. Combin. Theory Ser. B 60 (1994) 107 MR1256586
5	S V Chmutov, S V Duzhin, S K Lando, Vassiliev knot invariants I: Introduction, from: "Singularities and bifurcations", Adv. Soviet Math. 21, Amer. Math. Soc. (1994) 117 MR1310597
6	S V Chmutov, S V Duzhin, J Mostovoy, CDBooK. Introduction to Vassiliev Knot invariants (2007)
7	S V Chmutov, A N Varchenko, Remarks on the Vassiliev knot invariants coming from $\mathrm{sl}_2$, Topology 36 (1997) 153 MR1410469
8	B Courcelle, Circle graphs and Monadic Second-order logic, preprint (2005)
9	W H Cunningham, Decomposition of directed graphs, SIAM J. Algebraic Discrete Methods 3 (1982) 214 MR655562
10	J M Figueroa-O’Farrill, T Kimura, A Vaintrob, The universal Vassiliev invariant for the Lie superalgebra $\mathrm{gl}(1\|1)$, Comm. Math. Phys. 185 (1997) 93 MR1463035
11	C P Gabor, K J Supowit, W L Hsu, Recognizing circle graphs in polynomial time, J. Assoc. Comput. Mach. 36 (1989) 435 MR1072233
12	M Kontsevich, Vassiliev's knot invariants, from: "I. M. Gel'fand Seminar", Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 137 MR1237836
13	S K Lando, On a Hopf algebra in graph theory, J. Combin. Theory Ser. B 80 (2000) 104 MR1778203
14	S K Lando, A K Zvonkin, Graphs on surfaces and their applications, Encyclopaedia of Mathematical Sciences 141, Springer (2004) MR2036721
15	T Q T Le, J Murakami, The universal Vassiliev–Kontsevich invariant for framed oriented links, Compositio Math. 102 (1996) 41 MR1394520
16	B Mellor, Intersection graphs for string links, J. Knot Theory Ramifications 15 (2006) 53 MR2204497
17	H R Morton, P R Cromwell, Distinguishing mutants by knot polynomials, J. Knot Theory Ramifications 5 (1996) 225 MR1395780
18	J. Murakami, Finite type invariants detecting the mutant knots, from: "Knot Theory. A volume dedicated to Professor Kunio Murasugi for his 70th birthday" (editors M Sakuma, e al.) (2000)
19	C. Soulié, Complete invariant graphs of alternating knots arXiv:math.CO/0404490
20	A Vaintrob, Vassiliev knot invariants and Lie $S$–algebras, Math. Res. Lett. 1 (1994) 579 MR1295552
21	D J A Welsh, Matroid theory, London Math. Soc. Monographs 8, Academic Press (1976) MR0427112