3 problems

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Czap–Jendroľ–Valiska facial WORM coloring conjecture
Czap, Jendroľ and Valiska's conjecture. Every connected plane graph admits a $(P_{3},P_{4})$ -WORM coloring with $2$ colors.
Conjectureopengraph-coloring planar-graphs worm-coloringsarXiv posted 3 days ago
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Goddard–Wash–Xu lower-bound conjecture for K_3-WORM colorable graphs
Goddard–Wash–Xu conjecture. If $G$ is $K_3$ -WORM colorable, then
Conjecturesolvedgraph-coloring worm-coloringsarXiv posted 3 days ago
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Goddard–Wash–Xu's two-color conjecture for $K_3$ -WORM-colorable graphs
Let $G$ be a graph that admits a $K_3$ -WORM coloring, meaning a vertex coloring in which every copy of $K_3$ receives at least two colors. The $K_3$ -WORM lower chromatic number…
Conjecturerefutedchromatic-spectrum graph-coloring worm-coloringsarXiv posted 3 days ago

Czap–Jendroľ–Valiska facial WORM coloring conjecture