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Clique-width and well-quasi-ordering of triangle-free graph classes
Journal of Computer and System Sciences ( IF 1.129 ) 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.
更新日期:2020-01-04

 

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