Borodin Oleg Veniaminovich

Publications in Math-Net.Ru

1. Describing $3$-faces in $3$-polytopes without adjacent triangles
   
   Sibirsk. Mat. Zh., 66:1 (2025),  20–26
2. Describing edges incident with minor faces in 3-polytopes without adjacent 3-faces
   
   Mathematical notes of NEFU, 32:2 (2025),  50–55
3. Describing edges in normal plane maps having no adjacent $3$-faces
   
   Sib. Èlektron. Mat. Izv., 21:1 (2024),  495–500
4. Light $3$-paths in $3$-polytopes without adjacent triangles
   
   Sibirsk. Mat. Zh., 65:2 (2024),  249–257
5. Combinatorial structure of faces in triangulations on surfaces
   
   Sibirsk. Mat. Zh., 63:4 (2022),  796–804
6. Tight description of faces in torus triangulations with minimum degree 5
   
   Sib. Èlektron. Mat. Izv., 18:2 (2021),  1475–1481
7. All tight descriptions of major $3$-paths in $3$-polytopes without $3$-vertices
   
   Sib. Èlektron. Mat. Izv., 18:1 (2021),  456–463
8. A tight description of $3$-polytopes by their major $3$-paths
   
   Sibirsk. Mat. Zh., 62:3 (2021),  498–508
9. Heights of minor faces in 3-polytopes
   
   Sibirsk. Mat. Zh., 62:2 (2021),  250–268
10. Soft 3-stars in sparse plane graphs
    
    Sib. Èlektron. Mat. Izv., 17 (2020),  1863–1868
11. An extension of Franklin's Theorem
    
    Sib. Èlektron. Mat. Izv., 17 (2020),  1516–1521
12. All tight descriptions of $3$-paths in plane graphs with girth at least $8$
    
    Sib. Èlektron. Mat. Izv., 17 (2020),  496–501
13. All tight descriptions of $3$-paths centered at $2$-vertices in plane graphs with girth at least $6$
    
    Sib. Èlektron. Mat. Izv., 16 (2019),  1334–1344
14. Low faces of restricted degree in $3$-polytopes
    
    Sibirsk. Mat. Zh., 60:3 (2019),  527–536
15. Light minor $5$-stars in $3$-polytopes with minimum degree $5$
    
    Sibirsk. Mat. Zh., 60:2 (2019),  351–359
16. Light 3-stars in sparse plane graphs
    
    Sib. Èlektron. Mat. Izv., 15 (2018),  1344–1352
17. All tight descriptions of $3$-paths in plane graphs with girth at least $9$
    
    Sib. Èlektron. Mat. Izv., 15 (2018),  1174–1181
18. Describing neighborhoods of $5$-vertices in a class of $3$-polytopes with minimum degree $5$
    
    Sibirsk. Mat. Zh., 59:1 (2018),  56–64
19. Low and light $5$-stars in $3$-polytopes with minimum degree $5$ and restrictions on the degrees of major vertices
    
    Sibirsk. Mat. Zh., 58:4 (2017),  771–778
20. The height of faces of $3$-polytopes
    
    Sibirsk. Mat. Zh., 58:1 (2017),  48–55
21. Light neighborhoods of $5$-vertices in $3$-polytopes with minimum degree $5$
    
    Sib. Èlektron. Mat. Izv., 13 (2016),  584–591
22. Describing $4$-paths in $3$-polytopes with minimum degree $5$
    
    Sibirsk. Mat. Zh., 57:5 (2016),  981–987
23. Light and low $5$-stars in normal plane maps with minimum degree $5$
    
    Sibirsk. Mat. Zh., 57:3 (2016),  596–602
24. Heights of minor faces in triangle-free $3$-polytopes
    
    Sibirsk. Mat. Zh., 56:5 (2015),  982–987
25. Each $3$-polytope with minimum degree $5$ has a $7$-cycle with maximum degree at most $15$
    
    Sibirsk. Mat. Zh., 56:4 (2015),  775–789
26. The vertex-face weight of edges in $3$-polytopes
    
    Sibirsk. Mat. Zh., 56:2 (2015),  338–350
27. The weight of edge in 3-polytopes
    
    Sib. Èlektron. Mat. Izv., 11 (2014),  457–463
28. Combinatorial structure of faces in triangulated $3$-polytopes with minimum degree $4$
    
    Sibirsk. Mat. Zh., 55:1 (2014),  17–24
29. 2-distance 4-coloring of planar subcubic graphs
    
    Diskretn. Anal. Issled. Oper., 18:2 (2011),  18–28
30. Vertex decompositions of sparse graphs into an independent vertex set and a subgraph of maximum degree at most $1$
    
    Sibirsk. Mat. Zh., 52:5 (2011),  1004–1010
31. Acyclic 5-choosability of planar graphs without 4-cycles
    
    Sibirsk. Mat. Zh., 52:3 (2011),  522–541
32. Injective $(\Delta+1)$-coloring of planar graphs with girth 6
    
    Sibirsk. Mat. Zh., 52:1 (2011),  30–38
33. Acyclic 4-colorability of planar graphs without 4- and 5-cycles
    
    Diskretn. Anal. Issled. Oper., 17:2 (2010),  20–38
34. Acyclic $3$-choosability of planar graphs with no cycles of length from $4$ to $11$
    
    Sib. Èlektron. Mat. Izv., 7 (2010),  275–283
35. Acyclic 4-coloring of plane graphs without cycles of length 4 and 6
    
    Diskretn. Anal. Issled. Oper., 16:6 (2009),  3–11
36. Acyclic 3-choosability of plane graphs without cycles of length from 4 to 12
    
    Diskretn. Anal. Issled. Oper., 16:5 (2009),  26–33
37. Near-proper vertex 2-colorings of sparse graphs
    
    Diskretn. Anal. Issled. Oper., 16:2 (2009),  16–20
38. Partitioning sparse plane graphs into two induced subgraphs of small degree
    
    Sib. Èlektron. Mat. Izv., 6 (2009),  13–16
39. List 2-distance $(\Delta+2)$-coloring of planar graphs with girth 6 and $\Delta\ge24$
    
    Sibirsk. Mat. Zh., 50:6 (2009),  1216–1224
40. Высота цикла длины 4 в 1-планарных графах с минимальной степенью 5 без треугольников
    
    Diskretn. Anal. Issled. Oper., 15:1 (2008),  11–16
41. Circular $(5,2)$-coloring of sparse graphs
    
    Sib. Èlektron. Mat. Izv., 5 (2008),  417–426
42. List $2$-arboricity of planar graphs with no triangles at distance less than two
    
    Sib. Èlektron. Mat. Izv., 5 (2008),  211–214
43. Planar graphs without triangular $4$-cycles are $3$-choosable
    
    Sib. Èlektron. Mat. Izv., 5 (2008),  75–79
44. Предписанная 2-дистанционная $(\Delta+1)$-раскраска плоских графов с заданным обхватом
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 14:3 (2007),  13–30
45. Minimax degrees of quasiplane graphs without $4$-faces
    
    Sib. Èlektron. Mat. Izv., 4 (2007),  435–439
46. Decomposing a planar graph into a forest and a subgraph of restricted maximum degree
    
    Sib. Èlektron. Mat. Izv., 4 (2007),  296–299
47. Oriented 5-coloring of sparse plane graphs
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 13:1 (2006),  16–32
48. Sufficient conditions for the minimum $2$-distance colorability of plane graphs of girth $6$
    
    Sib. Èlektron. Mat. Izv., 3 (2006),  441–450
49. Planar graphs without triangles adjacent to cycles of length from $3$ to $9$ are $3$-colorable
    
    Sib. Èlektron. Mat. Izv., 3 (2006),  428–440
50. List $(p,q)$-coloring of sparse plane graphs
    
    Sib. Èlektron. Mat. Izv., 3 (2006),  355–361
51. Sufficient conditions for the 2-distance $(\Delta+1)$-colorability of planar graphs with girth 6
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 12:3 (2005),  32–47
52. An oriented colouring of planar graphs with girth at least $4$
    
    Sib. Èlektron. Mat. Izv., 2 (2005),  239–249
53. An oriented $7$-colouring of planar graphs with girth at least $7$
    
    Sib. Èlektron. Mat. Izv., 2 (2005),  222–229
54. A sufficient condition for the 3-colorability of plane graphs
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 11:1 (2004),  13–29
55. Sufficient conditions for planar graphs to be $2$-distance $(\Delta+1)$-colorable
    
    Sib. Èlektron. Mat. Izv., 1 (2004),  129–141
56. Continuation of a $3$-coloring from a $7$-face onto a plane graph without $3$-cycles
    
    Sib. Èlektron. Mat. Izv., 1 (2004),  117–128
57. $2$-distance coloring of sparse planar graphs
    
    Sib. Èlektron. Mat. Izv., 1 (2004),  76–90
58. Continuation of a 3-coloring from a 6-face to a plane graph without 3-cycles
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 10:3 (2003),  3–11
59. Strengthening Lebesgue's theorem on the structure of the minor faces in convex polyhedra
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 9:3 (2002),  29–39
60. On the continuation of a 3-coloring from two vertices in a plane graph without 3-cycles
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 9:1 (2002),  3–26
61. Estimating the Minimal Number of Colors in Acyclic -Strong Colorings of Maps on Surfaces
    
    Mat. Zametki, 72:1 (2002),  35–37
62. On the partition of a planar graph of girth 5 into an empty and an acyclic subgraph
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 8:4 (2001),  34–53
63. Minimal degrees and chromatic numbers of squares of planar graphs
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 8:4 (2001),  9–33
64. The structure of plane triangulations in terms of clusters and stars
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 8:2 (2001),  15–39
65. Distributive colorings of plane triangulations of minimum degree five
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 8:1 (2001),  3–16
66. On a structural property of plane graphs
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 7:4 (2000),  5–19
67. Acyclic $k$-strong coloring of maps on surfaces
    
    Mat. Zametki, 67:1 (2000),  36–45
68. Acyclic coloring of 1-planar graphs
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 6:4 (1999),  20–35
69. The height of small faces in planar normal maps
    
    Diskretn. Anal. Issled. Oper., Ser. 1, 5:4 (1998),  6–17
70. Weight of faces in plane maps
    
    Mat. Zametki, 64:5 (1998),  648–657
71. Colorings and topological representations of graphs
    
    Diskretn. Anal. Issled. Oper., 3:4 (1996),  3–27
72. Neighborhoods of edges in normal cards
    
    Diskretn. Anal. Issled. Oper., 2:3 (1995),  3–9
73. Structure of neighborhoods of edges in planar graphs and simultaneous coloring of vertices, edges and faces
    
    Mat. Zametki, 53:5 (1993),  35–47
74. Bidegree of graph and degeneracy number
    
    Mat. Zametki, 53:4 (1993),  13–20
75. A structural theorem on planar graphs and its application to coloring
    
    Diskr. Mat., 4:1 (1992),  60–65
76. Minimal weight of face in plane triangulations without 4-vertices
    
    Mat. Zametki, 51:1 (1992),  16–19
77. Joint generalization of the theorems of Lebesgue and Kotzig on the combinatorics of planar maps
    
    Diskr. Mat., 3:4 (1991),  24–27
78. On a characterization of chromatically rigid polynomials
    
    Sibirsk. Mat. Zh., 32:1 (1991),  22–27
79. Generalization of a theorem of Kotzig and a prescribed coloring of the edges of planar graphs
    
    Mat. Zametki, 48:6 (1990),  22–28
80. Solution of problems of Kotzig and Grünbaum concerning the isolation of cycles in planar graphs
    
    Mat. Zametki, 46:5 (1989),  9–12
81. A proof of Grünbaum's conjecture on the acyclic $5$-colorability of planar graphs
    
    Dokl. Akad. Nauk SSSR, 231:1 (1976),  18–20


82. In memory of Dmitry Germanovich Fon-Der-Flaass
    
    Sib. Èlektron. Mat. Izv., 7 (2010),  1–4