Geodesic
On a~bound on the chromatic number of almost planar graph
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part V, Tome 406 (2012), pp. 95-106

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Let $G$ be a graph, which can be drawn on the plane such that any edge intersects at most one other edge. We prove, that the chromatic number of $G$ does not exceed 7. We also prove the bound $\chi(G)\leq\frac{9+\sqrt{17+64g}}2$ for a graph $G$, which can be drawn on the surface of genus $g$, such that any edge intersects at most one other edge. 
@article{ZNSL_2012_406_a4,
     author = {G. V. Nenashev},
     title = {On a~bound on the chromatic number of almost planar graph},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--106},
     publisher = {mathdoc},
     volume = {406},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_406_a4/}
}
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G. V. Nenashev. On a~bound on the chromatic number of almost planar graph. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part V, Tome 406 (2012), pp. 95-106. http://geodesic.mathdoc.fr/item/ZNSL_2012_406_a4/