2 problems

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Conjectured relative clique number of triangle-free planar graphs
Triangle-free planar conjecture. For the family $\mathcal{P}_4$ of triangle-free planar graphs,
Conjectureopenclique-numbers graph-coloring planar-graphsarXiv posted 2 days ago
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Conjectured relative clique number of planar graphs of girth at least 3
Planar girth-three conjecture. For the family $\mathcal{P}_3$ of planar graphs,
Conjectureopenclique-numbers graph-coloring planar-graphsarXiv posted 2 days ago

Conjectured relative clique number of triangle-free planar graphs