Every planar multigraph has an induced forest of size at least n/4 (tight), with improved bounds of (2/5)n - k/10 when parallel-edge pairs are few and (3/10)n + 7/30 when 2-faces are forbidden.
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Large induced forests in planar multigraphs
Every planar multigraph has an induced forest of size at least n/4 (tight), with improved bounds of (2/5)n - k/10 when parallel-edge pairs are few and (3/10)n + 7/30 when 2-faces are forbidden.