Linear Clique-Width of Bi-complement Reducible Graphs

We prove that in the class of bi-complement reducible graphs linear clique-width is unbounded and show that this class contains exactly two minimal hereditary subclasses of unbounded linear clique-width.

[1]  Udi Rotics,et al.  Clique-Width is NP-Complete , 2009, SIAM J. Discret. Math..

[2]  Pinar Heggernes,et al.  Graphs of linear clique-width at most 3 , 2011, Theor. Comput. Sci..

[3]  Martin Charles Golumbic,et al.  Trivially perfect graphs , 1978, Discret. Math..

[4]  Vadim V. Lozin,et al.  The Clique-Width of Bipartite Graphs in Monogenic Classes , 2008, Int. J. Found. Comput. Sci..

[5]  Konrad Dabrowski,et al.  Classifying the clique-width of H-free bipartite graphs , 2016, Discret. Appl. Math..

[6]  Dieter Rautenbach,et al.  Chordal bipartite graphs of bounded tree- and clique-width , 2004, Discret. Math..

[7]  V. Giakoumakis,et al.  Bi-complement Reducible Graphs , 1997 .

[8]  Vadim V. Lozin,et al.  Minimal Classes of Graphs of Unbounded Clique-width and Well-quasi-ordering , 2015, ArXiv.

[9]  Robert Brignall,et al.  Linear Clique-Width for Hereditary Classes of Cographs , 2017, J. Graph Theory.

[10]  Vadim V. Lozin,et al.  Infinitely many minimal classes of graphs of unbounded clique-width , 2018, Discret. Appl. Math..

[11]  Mamadou Moustapha Kanté,et al.  Linear rank-width and linear clique-width of trees , 2015, Theor. Comput. Sci..

[12]  Gerard J. Chang,et al.  Quasi-threshold Graphs , 1996, Discret. Appl. Math..

[13]  Konrad Dabrowski,et al.  Bounding the clique-width of H-free split graphs , 2015, Discret. Appl. Math..

[14]  Pinar Heggernes,et al.  Characterising the linear clique-width of a class of graphs by forbidden induced subgraphs , 2012, Discret. Appl. Math..

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