论文信息 - Well-quasi-ordering Does Not Imply Bounded Clique-width

Well-quasi-ordering Does Not Imply Bounded Clique-width

We present a hereditary class of graphs of unbounded clique-width which is well-quasi-ordered by the induced subgraph relation. This result provides the negative answer to a question asked by Daligault, Rao and Thomasse in [3].

[1] Stéphan Thomassé,et al. Well-Quasi-Order of Relabel Functions , 2010, Order.

[2] Marko Petkovsek,et al. Letter graphs and well-quasi-order by induced subgraphs , 2002, Discret. Math..

[3] Joseph B. Kruskal,et al. The Theory of Well-Quasi-Ordering: A Frequently Discovered Concept , 1972, J. Comb. Theory A.

[4] Peter Damaschke,et al. Induced subgraphs and well-quasi-ordering , 1990, J. Graph Theory.

[5] Dieter Rautenbach,et al. The relative clique-width of a graph , 2007, J. Comb. Theory, Ser. B.

[6] Bruno Courcelle,et al. Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-Width , 2000, Theory of Computing Systems.

[7] Philippe Schnoebelen,et al. Well-structured transition systems everywhere! , 2001, Theor. Comput. Sci..

[8] Graham Higman,et al. Ordering by Divisibility in Abstract Algebras , 1952 .

[9] Frank Harary,et al. Graph Theory , 2016 .

[10] Paul D. Seymour,et al. Graph Minors. XX. Wagner's conjecture , 2004, J. Comb. Theory B.

[11] Stephan Kreutzer,et al. Lower Bounds for the Complexity of Monadic Second-Order Logic , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[12] Egon Wanke,et al. On the relationship between NLC-width and linear NLC-width , 2005, Theor. Comput. Sci..

[13] Vadim V. Lozin,et al. Two forbidden induced subgraphs and well-quasi-ordering , 2011, Discret. Math..