(3,3)-linked planar graphs (Q2519842)

A graph \(G\) is \((m,n)\)-linked if for any two disjoint subsets \(R,B\subseteq V(G)\) with \(| R| \leq m\) and \(| B|\leq n,\) \(G\) has two disjoint connected subgraphs containing \(R\) and \(B,\) respectively. The author shows that a planar graph with at least six vertices is \((3,3)\)-linked if and only if \(G\) is \(4\)-connected and maximal. A corollary states that if a planar graph \(G\) with at least six vertices is \((3,3)\)-linked, then \(G\) is \(4\)-ordered.