Geodesic
Non-extendible finite polycycles
Izvestiya. Mathematics, Tome 70 (2006) no. 1, pp. 1-18 
M. Deza; S. V. Shpektorov; M. I. Shtogrin. Non-extendible finite polycycles. Izvestiya. Mathematics, Tome 70 (2006) no. 1, pp. 1-18. http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a0/
@article{IM2_2006_70_1_a0,
     author = {M. Deza and S. V. Shpektorov and M. I. Shtogrin},
     title = {Non-extendible finite polycycles},
     journal = {Izvestiya. Mathematics},
     pages = {1--18},
     year = {2006},
     volume = {70},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a0/}
}
TY  - JOUR
AU  - M. Deza
AU  - S. V. Shpektorov
AU  - M. I. Shtogrin
TI  - Non-extendible finite polycycles
JO  - Izvestiya. Mathematics
PY  - 2006
SP  - 1
EP  - 18
VL  - 70
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a0/
LA  - en
ID  - IM2_2006_70_1_a0
ER  - 
%0 Journal Article
%A M. Deza
%A S. V. Shpektorov
%A M. I. Shtogrin
%T Non-extendible finite polycycles
%J Izvestiya. Mathematics
%D 2006
%P 1-18
%V 70
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a0/
%G en
%F IM2_2006_70_1_a0

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

We give a fairly simple proof of a result announced in [2] that there are only seven non-extendible finite $(r,q)$-polycycles: the tetrahedron without a face, the cube without a face, the octahedron without a face, the dodecahedron without a face, the icosahedron without a face, the split-vertex octahedron and the split-vertex icosahedron.

[1] Kharari F., Teoriya grafov, Mir, M., 1973 | MR | MR

[2] Deza M., Shtogrin M. I., “Ekstremalnye i nerasshiryaemye politsikly”, Tr. MIAN, 239, 2002, 127–145 | MR | Zbl

[3] Deza M., Shtogrin M., “Clusters of cycles”, J. of Geometry and Physics, 40 (2002), 302–319 | DOI | MR | Zbl

[4] Deza M., Shtogrin M. I., “Metrika postoyannoi krivizny na politsiklakh”, Matem. zametki, 78:2 (2005), 223–233 | MR | Zbl

[5] Zeifert G., Trelfall V., Topologiya, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001

[6] Novikov S. P., Topologiya, IKI, Moskva–Izhevsk, 2002