Two forbidden induced subgraphs and well-quasi-ordering |
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Authors: | Nicholas Korpelainen Vadim Lozin |
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Institution: | aDIMAP, University of Warwick, Coventry CV4 7AL, UK |
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Abstract: | It is known that a class of graphs defined by a single forbidden induced subgraph G is well-quasi-ordered by the induced subgraph relation if and only if G is an induced subgraph of P4. However, very little is known about well-quasi-ordered classes of graphs defined by more than one forbidden induced subgraph. We conjecture that for any natural number k, there are finitely many minimal classes of graphs defined by k forbidden induced subgraphs which are not well-quasi-ordered by the induced subgraph relation and prove the conjecture for k=2. We explicitly reveal many of the minimal classes defined by two forbidden induced subgraphs which are not well-quasi-ordered and many of those which are well-quasi-ordered by the induced subgraph relation. |
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Keywords: | Induced subgraph relation Well-quasi-order Antichain |
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