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Disjoint Paths in Graphs III, Characterization
Xingxing Yu
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA
yu@math.gatech.edu
Annals of Combinatorics 7 (2) p.229-246 June, 2003
AMS Subject Classification: 05C38
Abstract:
Let G be a graph, {a, b, c} V(G), and {a', b', c'} V(G) such that {a, b, c}{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 obstructions. As a consequence, we show that no obstruction can be 8-connected, unless b=b' or {a, c}={a', c'}.
Keywords: disjoint paths, 3-planar graph, connectivity

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