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Durham University

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Dabrowski, K.K., Lozin, V.V. & Paulusma, D. (2016), Well-quasi-ordering versus clique-width: new results on bigenic classes, in Mäkinen, Veli, Puglisi, Simon J. & Salmela, Leena eds, Lecture Notes in Computer Science 9843: 27th International Workshop on Combinatorial Algorithms (IWOCA 2016). Helsinki, Finland, Springer, Cham, Switzerland, 253-265.

Author(s) from Durham


Daligault, Rao and Thomassé conjectured that if a hereditary class of graphs is well-quasi-ordered by the induced subgraph relation then it has bounded clique-width. Lozin, Razgon and Zamaraev recently showed that this conjecture is not true for infinitely defined classes. For finitely defined classes the conjecture is still open. It is known to hold for classes of graphs defined by a single forbidden induced subgraph H, as such graphs are well-quasi-ordered and are of bounded clique-width if and only if H is an induced subgraph of P4P4. For bigenic classes of graphs i.e. ones defined by two forbidden induced subgraphs there are several open cases in both classifications. We reduce the number of open cases for well-quasi-orderability of such classes from 12 to 9. Our results agree with the conjecture and imply that there are only two remaining cases to verify for bigenic classes.