2 problems

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Győri–Paulos–Salia–Tompkins–Zamora even-cycle-free planar counting conjecture
Let $\ell\geq 2$ be an integer, let $p$ be a sufficiently large integer, let $H$ be the cycle of length $p$ , and let $\mathcal G$ be the class of all planar graphs with no even cyc…
Conjectureopencycle-counts extremal-graph-theory planar-graphsarXiv posted 3 days ago
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Generalized planar Turán conjecture for cycles with forbidden even cycles
Generalized cycle-count conjecture. For sufficiently large $k$ ,
Conjectureopencycle-counts extremal-graph-theory planar-graphsarXiv posted 3 days ago

Győri–Paulos–Salia–Tompkins–Zamora even-cycle-free planar counting conjecture