Parnostno barvanje povezav na licih po povezavah 2-povezanega ravninskega grafa, vloženega v ravnino, je barvanje povezav, pri katerem dve zaporedni povezavi na robu kakega lica prejmeta različni ...barvi. Dodatno zahtevamo, da je za vsako barvo ▫$c$▫ na robu vsakega lica število povezav barve ▫$c$▫ liho ali enako 0. Czap, Jendrol', Kardoš in Soták (2012) so pokazali, da vedno obstaja takšno barvanje s kvečjemu 20 barvami. To mejo smo znižali na 16.
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