Geodesic
Sufficient conditions for planar graphs to be $2$-distance $(\Delta+1)$-colorable
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 1 (2004), pp. 129-141

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

A trivial lower bound for the $2$-distance chromatic number $\chi_2(G)$ of any graph $G$ with maximum degree $\Delta$ is $\Delta+1$. We prove that if $G$ is planar and its girth is at least $7$, then $\chi_2(G)=\Delta+1$ whenever $\Delta\ge 30$. On the other hand, we construct planar graphs with girth $5$ and $6$ that have arbitrarily large $\Delta$ and $\chi_2(G)>\Delta+1$. 
@article{SEMR_2004_1_a11,
     author = {O. V. Borodin and A. N. Glebov and A. O. Ivanova and T. K. Neustroeva and V. A. Tashkinov},
     title = {Sufficient conditions for planar graphs to be $2$-distance $(\Delta+1)$-colorable},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {129--141},
     publisher = {mathdoc},
     volume = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2004_1_a11/}
}
TY  - JOUR
AU  - O. V. Borodin
AU  - A. N. Glebov
AU  - A. O. Ivanova
AU  - T. K. Neustroeva
AU  - V. A. Tashkinov
TI  - Sufficient conditions for planar graphs to be $2$-distance $(\Delta+1)$-colorable
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2004
SP  - 129
EP  - 141
VL  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2004_1_a11/
LA  - ru
ID  - SEMR_2004_1_a11
ER  - 
%0 Journal Article
%A O. V. Borodin
%A A. N. Glebov
%A A. O. Ivanova
%A T. K. Neustroeva
%A V. A. Tashkinov
%T Sufficient conditions for planar graphs to be $2$-distance $(\Delta+1)$-colorable
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2004
%P 129-141
%V 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2004_1_a11/
%G ru
%F SEMR_2004_1_a11
O. V. Borodin; A. N. Glebov; A. O. Ivanova; T. K. Neustroeva; V. A. Tashkinov. Sufficient conditions for planar graphs to be $2$-distance $(\Delta+1)$-colorable. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 1 (2004), pp. 129-141. http://geodesic.mathdoc.fr/item/SEMR_2004_1_a11/