2 problems

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The linear polychromatic coloring conjecture for hypergraph families
Let $\mathcal{H}$ be a hypergraph family, and let $m_\mathcal{H}(k)$ denote the minimum number of vertices needed to guarantee a polychromatic $k$ -coloring in the relevant hypergra…
Conjectureopenhitting-sets hypergraphs polychromatic-coloringarXiv posted 2 days ago
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The 2-shallow hitting set conjecture for pseudohalfsphere arrangements
Pseudohalfsphere hitting set conjecture. Every containment-free pseudohalfsphere arrangement has a $2$ -shallow hitting set. Consequently, using the stated algorithmic theorem, any…
Conjectureopenhitting-sets hypergraph-coloring pseudohalfplanesarXiv posted 2 days ago

The linear polychromatic coloring conjecture for hypergraph families