, Volume 35, Issue 2, pp 253–274 | Cite as

Well-Quasi-Ordering versus Clique-Width: New Results on Bigenic Classes

  • Konrad K. Dabrowski
  • Vadim V. Lozin
  • Daniël Paulusma
Open Access


Daligault, Rao and Thomassé asked whether a hereditary class of graphs well-quasi-ordered by the induced subgraph relation has bounded clique-width. Lozin, Razgon and Zamaraev recently showed that this is not true for classes defined by infinitely many forbidden induced subgraphs. However, in the case of finitely many forbidden induced subgraphs the question remains open and we conjecture that in this case the answer is positive. The conjecture 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 P 4. For bigenic classes of graphs, i.e. ones defined by two forbidden induced subgraphs, there are several open cases in both classifications. In the present paper we obtain a number of new results on well-quasi-orderability of bigenic classes, each of which supports the conjecture.


Well-quasi-order Induced subgraph Hereditary graph class Bigenic class 


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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Konrad K. Dabrowski
    • 1
  • Vadim V. Lozin
    • 2
  • Daniël Paulusma
    • 1
  1. 1.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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