Graphs Containing Topological H

Let H denote the tree with six vertices, two of which are adjacent and of degree 3. Let G be a graph andu 1 , u 2 , a 1 , a 2 , a 3 , a 4be distinct vertices of G . We characterize those G that contain a topological H in whichu 1 , u 2are of degree 3 anda 1 , a 2 , a 3 , a 4are of degree 1, which include all 5‐connected graphs. This work was motivated by the Kelmans–Seymour conjecture that 5‐connected nonplanar graphs contain topological K 5 .