Geodesic
An upper bound on the chromatic number of circle graphs without $K_4$
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part III, Tome 391 (2011), pp. 149-156

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Let $G$ be a circle graph without clique on 4 vertices. We proof that the chromatic number of $G$ doesn't exceed 30. 
@article{ZNSL_2011_391_a6,
     author = {G. V. Nenashev},
     title = {An upper bound on the chromatic number of circle graphs without $K_4$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--156},
     publisher = {mathdoc},
     volume = {391},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_391_a6/}
}
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G. V. Nenashev. An upper bound on the chromatic number of circle graphs without $K_4$. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part III, Tome 391 (2011), pp. 149-156. http://geodesic.mathdoc.fr/item/ZNSL_2011_391_a6/