Geodesic
An oriented colouring of planar graphs with girth at least~$4$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 239-249

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An oriented $k$-colouring of an oriented graph $H$ is a homomorphism of $H$ into a tournament on $k$ vertices. In the paper we prove that any orientation of a planar graph without triangle has an oriented $47$-colouring, which improves the best known upper bound $59$. 
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     author = {O. V. Borodin and A. O. Ivanova},
     title = {An oriented colouring of planar graphs with girth at least~$4$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {239--249},
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     year = {2005},
     language = {ru},
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O. V. Borodin; A. O. Ivanova. An oriented colouring of planar graphs with girth at least~$4$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 239-249. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a17/