Proves two CISTs exist in every 3-connected 2-outerplanar triangulated disc, supplies conditions for 3-outerplanar cases, and exhibits a 4-outerplanar counterexample.
Araki, Dirac’s condition for completely independent spanning trees, Journal of Graph Theory 77 (3) (2014) 171–179
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Completely Independent Spanning Trees in $k$-Outerplanar Triangulated Discs
Proves two CISTs exist in every 3-connected 2-outerplanar triangulated disc, supplies conditions for 3-outerplanar cases, and exhibits a 4-outerplanar counterexample.