Graph minors. III. Planar tree-width

Neil Robertson, P.D Seymour
1984 Journal of combinatorial theory. Series B (Print)  
The "tree-width" of a graph is defined and it is proved that for any fixed planar graph H, every planar graph with sutliciently large tree-width has a minor isomorphic to H. This result has several applications which are described in other papers in this series.
doi:10.1016/0095-8956(84)90013-3 fatcat:345gc7o3d5f3he4nkelsxcgu7e