Knauer and Micek build cubic planar graphs with faces of length at most 7 and diameter O(log n), disproving the suspected square-root lower bound for bounded-face cubic planar graphs.
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Planar cubic graphs of small diameter
Knauer and Micek build cubic planar graphs with faces of length at most 7 and diameter O(log n), disproving the suspected square-root lower bound for bounded-face cubic planar graphs.