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

Autor:	Dabrowski, Konrad K., Lozin, Vadim V., Paulusma, Daniël
Rok vydání:	2016
Předmět:	Mathematics - Combinatorics Computer Science - Discrete Mathematics Computer Science - Data Structures and Algorithms
Druh dokumentu:	Working Paper
Popis:	Daligault, Rao and Thomass\'e 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. Comment: 26 pages, 3 figures. An extended abstract of this paper appeared in the proceedings of IWOCA 2016
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1611.03671 Zobrazit plný text záznamu View this record from Arxiv