Strong tree-cographs are Birkoff graphs
Discrete Applied Mathematics
A tree representation for P4-sparse graphs
Discrete Applied Mathematics
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Discrete Mathematics
Regular Article: Bi-complement Reducible Graphs
Advances in Applied Mathematics
Proceedings of an international symposium on Graphs and combinatorics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Clique-Width of Graphs in Hereditary Classes
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Investigating the b-chromatic number of bipartite graphs by using the bicomplement
Discrete Applied Mathematics
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A graph is called complement reducible (a cograph for short) if every its induced subgraph with at least two vertices is either disconnected or the complement to a disconnected graph. The bipartite analog of cographs, bi-complement reducible graphs, has been characterized recently by three forbidden induced subgraphs: Star1,2,3, Sun4 and P7, where Star1,2,3 is the graph with vertices a, b, c, d, e, f, g and edges (a, b), (b, c), (c, d), (d, e), (e, f), (d, g), and Sun4 is the graph with vertices a, b, c, d, e, f, g, h and edges (a, b), (b, c), (c, d), (d, a), (a, e), (b, f), (c, g), (d, h). In the present paper, we propose a structural characterization for the class of bipartite graphs containing no graphs Star1,2,3 and Sun4 as induced subgraphs. Based on the proposed characterization we prove that the clique-width of these graphs is at most five that leads to polynomial algorithms for a number of problems which are NP-complete in general bipartite graphs.