Classifying the Clique-Width of H-Free Bipartite Graphs
Let G be a bipartite graph, and let H be a bipartite graph with a fixed bipartition (BH,WH). We consider three different, natural ways of forbidding H as an induced subgraph in G. First, G is H-free if it does not contain H as an induced subgraph. Second, G is strongly H-free if G is H-free or else has no bipartition (BG,WG) with BH ⊆ BG and WH ⊆ WG. Third, G is weakly H-free if G is H-free or else has at least one bipartition (BG,WG) with \(B_H\not\subseteq B_G\) or \(W_H\not\subseteq W_G\). Lozin and Volz characterized all bipartite graphs H for which the class of strongly H-free bipartite graphs has bounded clique-width. We extend their result by giving complete classifications for the other two variants of H-freeness.
Unable to display preview. Download preview PDF.
- 2.Bonomo, F., Grippo, L.N., Milanič, M., Safe, M.D.: Graphs of power-bounded clique-width. arXiv, abs/1402.2135 (2014)Google Scholar
- 12.Dabrowski, K.K., Paulusma, D.: Clique-width of graph classes defined by two forbidden induced subgraphs. coRR, abs/1405.7092 (2014)Google Scholar
- 13.Gurski, F.: Graph operations on clique-width bounded graphs. CoRR, abs/cs/0701185 (2007)Google Scholar
- 20.Oum, S.-I.: Approximating rank-width and clique-width quickly. ACM Trans. Algorithms 5(1), 10:1–10:20 (2008)Google Scholar