Extending a Skew -Partition

When can a skew partition of an induced subgraph be extended to a skew partition of G? Algorithmically this is answered by the algorithm of de Figueiredo, Klein, Kohayakawa and Reed [ MR 2001j:05114], but what about a theorem? Is there some theorem that says ``either the skew partition is extendable, or there is a reason why not (an obstruction)"? Contributed by Paul Seymour

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