Diagram approach in the theory of knots and its application in the graph theory
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 65-71 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is a review of the results of the eponymous cycle of authors' works marked by the prize of I. I. Shuvalov of the I degree for scientific activity.
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D. P. Il'yutko; I. M. Nikonov. Diagram approach in the theory of knots and its application in the graph theory. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 65-71. http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a10/

[1] Manturov V.O., Ilyutko D.P., Virtual Knots. The State of the Art, World Scientific Publishing Co, Singapore, 2013 | MR | Zbl

[2] Ilyutko D.P., Trofimova A.D., “2-Colored diagrams of knots”, Lobachevskii J. Math., 38:6 (2017), 987–997 | DOI | MR | Zbl

[3] Manturov V.O., “Chetnost v teorii uzlov”, Matem. sb., 201:5 (2010), 65–110 | DOI | MR

[4] Ilyutko D.P., Manturov V.O., Nikonov I.M., “Chetnost v teorii uzlov i graf-zatsepleniya”, Sovremennaya matematika. Fundamentalnye napravleniya, 41 (2011), 3–163

[5] Ilyutko D.P., Safina V.S., “Graf-zatsepleniya: nerealizuemost, orientatsiya i polinom Dzhonsa”, Sovremennaya matematika. Fundamentalnye napravleniya, 51 (2014), 33–63

[6] Khovanov M., “A categorification of the Jones polynomial”, Duke Math. J., 101:3 (2000), 359–426 | DOI | MR | Zbl

[7] Kronheimer P.B., Mrowka T.S., “Khovanov homology is an unknot-detector”, Publications mathematiques de l'IHES, 113:1 (2011), 97–208 | DOI | MR | Zbl

[8] Nikonov I.M., “Nechetnye gomologii Khovanova glavno unimodulyarnykh dvudolnykh graf-zatseplenii”, Tr. semin. po vektornomu i tenzornomu analizu s ikh prilozheniem k geometrii, mekhanike i fizike, XXVIII, 2012, 211–249

[9] Ilyutko D.P., Manturov V.O., Nikonov I.M., Parity and Patterns in Low-Dimensional Topology, Cambridge Scientific Publishers, Cambridge, 2015 | MR

[10] Nikonov I.M., “A new proof of Vassiliev's conjecture”, J. Knot Theory and its Ramifications, 23:7 (2014) | DOI | MR | Zbl