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No, it is not linear in the genus; it is at least exponential in $g$. See for example this answeranswer by David Eppstein.

No, it is not linear in the genus; it is at least exponential in $g$. See for example this answer by David Eppstein.

No, it is not linear in the genus; it is at least exponential in $g$. See for example this answer by David Eppstein.

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Tony Huynh
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No, it is not linear in the genus; it is at least exponential in $g$. See for example this answer by David Eppstein.