Every 4-connected plane triangulation on at least 7 vertices has at least |V≥5| + 2 edges whose contraction preserves 4-connectedness, and the extremal graphs are determined.
Martinov, Uncontractible 4-connected graphs, Journal of Graph Theory 6 (1982), 343–344
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On the number of 4-contractible edges in plane triangulations
Every 4-connected plane triangulation on at least 7 vertices has at least |V≥5| + 2 edges whose contraction preserves 4-connectedness, and the extremal graphs are determined.