2 problems

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Fong–Chan–Nong conjecture on trees with path forests of degree-four vertices
Let $T$ be a tree with maximum degree $4$ , and let the subgraph of $T$ induced by all its degree-four vertices be a forest of paths of length $l$ . Fong–Chan–Nong conjecture. The tr…
Conjectureopengame-coloring graph-coloring treesarXiv posted 2 days ago
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The finiteness threshold for asymmetric game chromatic numbers of posets
Let $\mathcal{P}=(P,\leq)$ be a poset of width $w$ , and let $\chi_{\mathrm{g}}(a,b,w)$ denote the maximum of the $(a,b)$ -game chromatic number over all posets of width $w$ . Finiten…
Conjectureopengame-coloring incomparability-graphs posetsarXiv posted 2 days ago

Fong–Chan–Nong conjecture on trees with path forests of degree-four vertices