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The diagram approach in knot theory and applications to graph theory. (English. Russian original) Zbl 1400.57003
Mosc. Univ. Math. Bull. 73, No. 3, 124-130 (2018); translation from Vestn. Mosk. Univ., Ser. I 73, No. 3, 65-71 (2018).
Summary: The paper is a survey of a series of publications of the authors awarded by I. I Shuvalov First Prize of Lomonosov Moscow State University for scientific activity, 2017.
MSC:
57M15 Relations of low-dimensional topology with graph theory
05C10 Planar graphs; geometric and topological aspects of graph theory
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References:
[1] V. O. Manturov and D. P. Ilyutko, Virtual Knots. The St,ate of the Art (World Sei. Publ. Co, Singapore, 2013). · Zbl 1270.57003
[2] Ilyutko, D. P.; Trofimova, A. D., 2-colored diagrams of knots, Lobachevskii J. Math., 38, 987, (2017) · Zbl 1404.57012
[3] Manturov, V. O., Parity in knot theory, Matem. Sbornik, 201, 65, (2010) · Zbl 1210.57010
[4] Ilyutko, D. P.; Manturov, V. O.; Nikonov, I. M., Parity in knot theory and graph-links, Contem. Math. Fundamental Directions, 41, 3, (2011) · Zbl 1320.57001
[5] Ilyutko, D. P.; Safina, V. S., Graph-links: nonrealizability, orientation, and Jones polynomial, Contem. Math. Fundamental Directions, 51, 33, (2014) · Zbl 1337.05025
[6] Khovariov, M., A categorificatiori of the Jones polynomial, Duke Math. J., 101, 359, (2000) · Zbl 0960.57005
[7] Kronheimer, P. B.; Mrowka, T. S., Khovanov homology is an unknot-detector, Pub. Math, de 1’IHES, 113, 97, (2011) · Zbl 1241.57017
[8] I. M. Nikonov, “Odd Khovanov Homology of Principally Unimodular Bipartite Graph-Links,” Trudy Semin. Vektorn. Tenzor. Anal. Prilozhen. Geom., Mekhan., Fiz. XXVIII, 211 (2012) [in Russian] (arXiv: 1006.0161).
[9] D. P. Ilyutko, V. O. Manturov, and I. M. Nikonov, Parity and Patterns in Low-Dimensional Topology (Cambridge Sei. Publ., Cambridge, 2015). · Zbl 1387.57025
[10] I. M. Nikonov, “A New Proof of Vassiliev’s Conjecture,” J. Knot Theory and its Ramifications 23 (7), (2014). · Zbl 1302.05043
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