(3,3)-Linked planar graphs

Ryuichi Mori
2008 Discrete Mathematics  
A graph G is (m, n)-linked if for any two disjoint subsets R, B ⊂ V (G) with |R| m and |B| n, G has two disjoint connected subgraphs containing R and B, respectively. We shall prove that a planar graph with at least six vertices is (3, 3)-linked if and only if G is 4-connected and maximal.
doi:10.1016/j.disc.2007.09.013 fatcat:2tj3ezsitnenfet6jjm7v5wmym