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JOURNALS // Sibirskii Matematicheskii Zhurnal
Sibirsk. Mat. Zh., 2021, Volume 62, Number 2, Pages 250–268 (Mi smj7554)
Heights of minor faces in 3-polytopes
O. V. Borodin, A. O. Ivanova

References
1. Steinitz E., “Polyeder und Raumeinteilungen”, Enzykl. math. Wiss. (Geometrie), 3AB, 12 (1922), 1–139
2. Lebesgue H., “Quelques conséquences simples de la formule d'Euler”, J. Math. Pures Appl., 19 (1940), 27–43  mathscinet
3. Borodin O. V., “Colorings of plane graphs: a survey”, Discrete Math., 313:4 (2013), 517–539  crossref  mathscinet  zmath  elib
4. Plummer M. D., Toft B., “Cyclic coloration of 3-polytopes”, J. Graph Theory, 11 (1987), 507–515  crossref  mathscinet  zmath
5. Ore O., Plummer M. D., “Cyclic coloration of plane graphs”, Recent progress in combinatorics, Acad. Press, New York, 1969, 287–293  mathscinet
6. Borodin O. V., “Usilenie teoremy Lebega o stroenii mladshikh granei v vypuklykh mnogogrannikakh”, Diskret. analiz i issled. operatsii, 9:3 (2002), 29–39  mathnet  zmath
7. Borodin O. V., Ivanova A. O., “Describing 3-faces in normal plane maps with minimum degree 4”, Discrete Math., 313:23 (2013), 2841–2847  crossref  mathscinet  zmath  elib
8. Borodin O. V., Ivanova A. O., Kostochka A. V., “Describing faces in plane triangulations”, Discrete Math., 319 (2014), 47–61  crossref  mathscinet  zmath  elib
9. Borodin O. V., Ivanova A. O., “Describing faces in 3-polytopes with no vertices of degree from 5 to 7”, Discrete Math., 342:11 (2019), 3208–3215  crossref  mathscinet  zmath
10. Kotzig A., “From the theory of Eulerian polyhedra”, Mat. Čas., 13 (1963), 20–31  mathscinet
11. Borodin O. V., “Reshenie zadach Kotsiga i Gryunbauma ob otdelimosti tsikla v ploskom grafe”, Mat. zametki, 46:5 (1989), 9–12  mathnet  mathscinet
12. Grünbaum B., “Polytopal graphs”, Studies in graph theory, MAA Studies in Mathematics, 12, 1975, 201–224  mathscinet  zmath
13. Plummer M. D., “On the cyclic connectivity of planar graphs”, Graph theory and applications, Proceedings of the Conference at Western Michigan University, Lecture Notes in Mathematics, 303, Springer-Verl., Berlin–Heidelberg, 1972, 235–242  crossref  mathscinet
14. Kotzig A., “Extremal polyhedral graphs”, Ann. New York Acad. Sci., 319 (1979), 569–570
15. Borodin O. V., “Minimalnyi ves grani v ploskikh triangulyatsiyakh bez 4-vershin”, Mat. zametki, 51:1 (1992), 16–19  mathnet  mathscinet  zmath
16. Borodin O. V., “Triangulated 3-polytopes with restricted minimal weight of faces”, Discrete Math., 186 (1998), 281–285  crossref  mathscinet  zmath
17. Avgustinovich S. V., Borodin O. V., “Okrestnosti reber v normalnykh kartakh”, Diskret. analiz i issled. operatsii, 2:3 (1995), 3–9  mathnet  mathscinet
18. Borodin O. V., Ivanova A. O., “Low edges in 3-polytopes”, Discrete Math., 338:12 (2015), 2234–2241  crossref  mathscinet  zmath  elib
19. Horňák M., Jendrol' S., “Unavoidable sets of face types for planar maps”, Discuss. Math. Graph Theory, 16:2 (1996), 123–142  crossref  mathscinet
20. Borodin O. V., Vudal D. R., “Ves granei v ploskikh kartakh”, Mat. zametki, 64:5 (1998), 648–657  mathnet  mathscinet  zmath
21. Borodin O. V., Ivanova A. O., “Vysota granei 3-mnogogrannikov”, Sib. mat. zhurn., 58:1 (2017), 48–55  mathnet  mathscinet  zmath
22. Borodin O. V., Bykov M. A., Ivanova A. O., “More about the height of faces in 3-polytopes”, Discuss. Mat. Graph Theory, 38:2 (2018), 443–453  crossref  mathscinet  zmath
23. Borodin O. V., Ivanova A. O., “Low minor faces in 3-polytopes”, Discrete Math., 341:12 (2018), 3415–3424  crossref  mathscinet  zmath
24. Borodin O. V., Loparev D. V., “Vysota mladshikh granei v ploskikh normalnykh kartakh”, Diskpet. analiz i issled. opepatsii, 5:4 (1998), 6–17  mathnet  mathscinet  zmath
25. Borodin O. V., Ivanova A. O., “Vysota malykh granei v 3-mnogogrannikakh bez treugolnikov”, Sib. mat. zhurn., 56:5 (2015), 982–988  mathnet  mathscinet  zmath
26. Jendrol' S., Voss H.-J., “Light subgraphs of graphs embedded in the plane — a survey”, Discrete Math., 313:4 (2013), 406–421  crossref  mathscinet  zmath
27. Borodin O. V., Ivanova A. O., “New results about the structure of plane graphs: a survey”, AIP Conference Proceedings, 1907:1 (2017), 030051  crossref  mathscinet
28. Mohar B., Škrekovski R., Voss H.-J., “Light subgraphs in planar graphs of minimum degree 4 and edge-degree 9”, J. Graph Theory, 44:4 (2003), 261–295  crossref  mathscinet  zmath
29. Jendrol' S., “Triangles with restricted degrees of their boundary vertices in plane triangulations”, Discrete Math., 196 (1999), 177–196  crossref  mathscinet  zmath
30. Borodin O. V., “Sovmestnoe obobschenie teorem Lebega i Kotsiga o kombinatorike ploskikh grafov”, Diskret. matematika, 3:4 (1991), 24–27  mathnet  mathscinet  zmath
31. Borodin O. V., Ivanova A. O., “The height of edge in 3-polytope”, Sib. Elektron. Mat. Izv., 11 (2014), 457–463  mathnet  mathscinet  zmath
32. Borodin O. V., Woodall D. R., “Cyclic degrees of 3-polytopes”, Graphs Combin., 15 (1999), 267–277  crossref  mathscinet  zmath
33. Ferencová B., Madaras T., “On the structure of polyhedral graphs with prescribed edge and dual edge weight”, Acta Univ. M. Belii Math., 12 (2005), 13–18  mathscinet  zmath
34. Ferencová B., Madaras T., “Light graph in families of polyhedral graphs with prescribed minimum degree, face size, edge and dual edge weight”, Discrete Math., 310 (2010), 1661–1675  crossref  mathscinet  zmath
35. Kotzig A., “Contribution to the theory of Eulerian polyhedra”, Mat.-Fyz. Casopis, 5 (1995), 101–113  mathscinet
36. Madaras T., Škrekovski R., “Heavy paths, light stars, and big melons”, Discrete Math., 286 (2004), 115–131  crossref  mathscinet  zmath

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