2 problems

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Erdős's equitable coloring conjecture for graphs
Erdős's conjecture. Every graph $G$ with maximal vertex degree $\Delta(G)$ admits not only a proper but also an equitable coloring with $\Delta(G)+1$ colors.
Conjectureopenequitable-colorings graph-coloringarXiv posted 2 days ago
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The $Er{s}$ –Hajnal–Szemerédi skewed coloring conjecture
Skewed coloring conjecture. If
Conjectureopenequitable-colorings extremal-combinatorics graph-coloringarXiv posted 2 days ago

Erdős's equitable coloring conjecture for graphs