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11. Planar-critical graphs

    1. Planar-critical graphs

          A graph is said to be $k$-planar if it can be drawn with at most $k$ crossing on each edge. A graph is said to be $m$-planar-critical if it is not $m$-planar but removal of any edge makes it $m$-planar.

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      Problem 11.1.

      [Geza Toth] Is there a constant $k$ such that every $1$-planar-critical graph is $k$-planar?
          Note: If this statement is true, then for any $m \geq 1$, there is a constant $k$ such that every $m$-planar-critical graph is $k$-planar.

          Cite this as: AimPL: Albertson conjecture and related problems, available at http://aimpl.org/albertson.