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Clique-width and well-quasi-ordering of triangle-free graph classes
Journal of Computer and System Sciences ( IF 1.1 ) Pub Date : 2019-09-26 , DOI: 10.1016/j.jcss.2019.09.001
Konrad K. Dabrowski , Vadim V. Lozin , Daniël Paulusma

We obtain a complete classification of graphs H for which the class of (triangle,H)-free graphs is well-quasi-ordered by the induced subgraph relation and an almost complete classification of graphs H for which the class of (triangle,H)-free graphs has bounded clique-width. In particular, we show that for these graph classes, well-quasi-orderability implies boundedness of clique-width. To obtain our results, we further refine a known method based on canonical decomposition. This leads to a new decomposition technique that is applicable to both notions, well-quasi-orderability and clique-width.



中文翻译:

无三角形图类的类宽度和良好拟序

我们获得图H的完全分类,其中三角形H诱导子图关系和图H的几乎完整分类对无图是很好的拟序,对于三角形H无图具有界线宽度。特别地,我们表明对于这些图类,良好的可排序性暗示了集团宽度的有界性。为了获得我们的结果,我们进一步完善了基于规范分解的已知方法。这导致了一种新的分解技术,该技术适用于两种概念:准拟序性和集团宽度。

更新日期:2019-09-26
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