Geodesic
Spatial graphs, tangles and plane trees
Algebra i analiz, Tome 31 (2019) no. 6, pp. 197-207.

Voir la notice de l'article provenant de la source Math-Net.Ru

All (finite connected) spatial graphs are supplied with an additional structure – the replenished skeleton and its disk framing, – in such a way that the problem of isotopic classification of spatial graphs endowed with this structure admits reduction to two problems: the (classical) problem of isotopic classification of tangles and the (close to classical) problem of isotopic classification of plane trees equipped with an additional structure, specifically, a set of hanging vertices and a fixed vertex (the root of the tree) in this set.
Keywords: chord diagram, tangle, plane tree, spacial graph, spacial tortoise, smooth isotopy. 
@article{AA_2019_31_6_a4,
     author = {V. M. Nezhinskij},
     title = {Spatial graphs, tangles and plane trees},
     journal = {Algebra i analiz},
     pages = {197--207},
     publisher = {mathdoc},
     volume = {31},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2019_31_6_a4/}
}
TY  - JOUR
AU  - V. M. Nezhinskij
TI  - Spatial graphs, tangles and plane trees
JO  - Algebra i analiz
PY  - 2019
SP  - 197
EP  - 207
VL  - 31
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2019_31_6_a4/
LA  - ru
ID  - AA_2019_31_6_a4
ER  - 
%0 Journal Article
%A V. M. Nezhinskij
%T Spatial graphs, tangles and plane trees
%J Algebra i analiz
%D 2019
%P 197-207
%V 31
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2019_31_6_a4/
%G ru
%F AA_2019_31_6_a4
V. M. Nezhinskij. Spatial graphs, tangles and plane trees. Algebra i analiz, Tome 31 (2019) no. 6, pp. 197-207. http://geodesic.mathdoc.fr/item/AA_2019_31_6_a4/

[1] Maslova Yu. V., Nezhinskii V. M., “Osnascheniya maksimalnykh derevev parami khord”, Zap. nauch. semin. POMI, 415, 2013, 91–102

[2] Moriuchi H., “A table of handcuff graphs with up to seven crossings”, Knot Theory for Scientific Objects, OCAMI Stud., 1, 2007, 179–200 | MR | Zbl

[3] Moriuchi H., “Enumeration of algebraic tangles with applications to theta-curves and handcuff graphs”, Kyungpook Math. J., 48:3 (2008), 337–357 | DOI | MR | Zbl

[4] Moriuchi H., “An enumeration of theta-curves with up to seven crossings”, J. Knot Theory Ramifications, 18:2 (2009), 167–197 | DOI | MR | Zbl

[5] Nezhinskii V. M., Maslova Yu. V., “Zatsepleniya vershinno osnaschennykh grafov”, Vestn. SPb. un-ta. Ser. mat., mekh., astronom., 2012, no. 2, 57–60

[6] Nezhinskii V. M., Maslova Yu. V., “Vershinno osnaschennye grafy”, Zap. nauch. semin. POMI, 415, 2013, 103–108

[7] Nezhinskii V. M., Maslova Yu. V., “Osnascheniya prostranstvennykh grafov”, Zap. nauch. semin. POMI, 464, 2017, 88–94

[8] Oyamaguchi N., “Enumeration of spatial $2$-bouquet graphs up to flat vertex isotopy”, Topology Appl., 196 (2015), 805–814 | DOI | MR | Zbl

[9] Palais R. S., “Extending diffeomorphisms”, Proc. Amer. Math. Soc., 11 (1960), 274–277 | DOI | MR | Zbl

[10] Kharari F., Teoriya grafov, KomKniga, M., 2006

[11] Khirsh M., Differentsialnaya topologiya, Mir, M., 1979