Geodesic
Joint generalization of the theorems of Lebesgue and Kotzig on the combinatorics of planar maps
Diskretnaya Matematika, Tome 3 (1991) no. 4, pp. 24-27.

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

The weight of an edge in a map or polyhedron is the sum of the degrees of its end points. A map is normal if it does not contain vertices or faces incident to fewer than three edges. We prove that every planar normal map contains the following: either a 3-face incident to an edge of weight no greater than 13; or a 4-face incident to an edge of weight no greater than 8; or a 5-face incident to an edge of weight 6. All the bounds – 13, 8 and 6 – are attainable. 
@article{DM_1991_3_4_a3,
     author = {O. V. Borodin},
     title = {Joint generalization of the theorems of {Lebesgue} and {Kotzig} on the combinatorics of planar maps},
     journal = {Diskretnaya Matematika},
     pages = {24--27},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1991_3_4_a3/}
}
TY  - JOUR
AU  - O. V. Borodin
TI  - Joint generalization of the theorems of Lebesgue and Kotzig on the combinatorics of planar maps
JO  - Diskretnaya Matematika
PY  - 1991
SP  - 24
EP  - 27
VL  - 3
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_1991_3_4_a3/
LA  - ru
ID  - DM_1991_3_4_a3
ER  - 
%0 Journal Article
%A O. V. Borodin
%T Joint generalization of the theorems of Lebesgue and Kotzig on the combinatorics of planar maps
%J Diskretnaya Matematika
%D 1991
%P 24-27
%V 3
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_1991_3_4_a3/
%G ru
%F DM_1991_3_4_a3
O. V. Borodin. Joint generalization of the theorems of Lebesgue and Kotzig on the combinatorics of planar maps. Diskretnaya Matematika, Tome 3 (1991) no. 4, pp. 24-27. http://geodesic.mathdoc.fr/item/DM_1991_3_4_a3/