3 problems

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The improper 4-coloring conjecture for toroidal graphs with defect sequence $(0,0,0,3)$
Improper coloring conjecture for toroidal graphs. Every toroidal graph is $(0,0,0,3)$ -colorable.
Conjectureopengraph-coloring improper-coloring toroidal-graphsarXiv posted 2 days ago
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Equality of the d-improper chromatic number and chromatic number under strong product with a clique
The d-improper chromatic product conjecture. The corresponding integral equality should also hold:
Conjectureopengraph-coloring improper-coloring strong-productsarXiv posted 2 days ago
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Yan et al.'s Ohba-like conjecture for improper colorings
Let $G$ be a graph and let $d$ be a nonnegative integer. Let $\chi^d(G)$ and $\chi_l^d(G)$ denote respectively the $d$ -improper chromatic number and the $d$ -improper list chromatic…
Conjecturesolvedgraph-coloring improper-coloring list-coloringarXiv posted 2 days ago

The improper 4-coloring conjecture for toroidal graphs with defect sequence (0,0,0,3)(0,0,0,3)(0,0,0,3)