Toroidal graphs without $K_5^{-}$ and 6-cycles

Ping Chen, Tao Wang

Cai et al.\ proved that a toroidal graph $G$ without $6$-cycles is $5$-choosable, and proposed the conjecture that $\text{ch}(G)=5$ if and only if $G$ contains a $K_5$ [J. Gr…