Disjoint Paths in Graphs II,A Special Case

Abstract. Let G be a graph,$ \{a,b,c\}\subseteq V(G) $, and $ \{a',b',c'\}\subseteq V(G) $ such that $ \{a,b,c\}\neq \{a',b',c'\} $. We say that $ (G,\{a,c\}, \{a',c'\}, (b, b')) $ is an obstruction if, for any three vertex disjoint paths from {a, b, c} to {a', b', c'} in G, one path is from b to b'. In this paper, we characterize a special class of obstructions. This will be used to characterize all obstructions.