Geodesic
Planar graphs without triangles adjacent to cycles of length from~$3$ to~$9$ are $3$-colorable
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 428-440

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Planar graphs without triangles adjacent to cycles of length from $3$ to $9$ are proved to be $3$-colorable, which extends Grötzsch's theorem. We conjecture that planar graphs without $3$-cycles adjacent to cycles of length $3$ or $5$ are $3$-colorable. 
@article{SEMR_2006_3_a27,
     author = {O. V. Borodin and A. N. Glebov and T. R. Jensen and A. Raspaud},
     title = {Planar graphs without triangles adjacent to cycles of length from~$3$ to~$9$ are $3$-colorable},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {428--440},
     publisher = {mathdoc},
     volume = {3},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2006_3_a27/}
}
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O. V. Borodin; A. N. Glebov; T. R. Jensen; A. Raspaud. Planar graphs without triangles adjacent to cycles of length from~$3$ to~$9$ are $3$-colorable. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 428-440. http://geodesic.mathdoc.fr/item/SEMR_2006_3_a27/