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Complexity of minimum biclique cover and minimum biclique decomposition for bipartite domino-free graphs. (English) Zbl 0906.05067
A bipartite graph is domino-free if it does not contain a 6-cycle with exactly one chord. Bipartite domino-free graphs can be recognized in time $$O(nm)$$. A biclique cover (biclique decomposition) of a graph $$G$$ is a family of complete bipartite subgraphs of $$G$$ whose edges cover (partition) the edge set of $$G$$. The minimum cardinalities of a biclique cover and a biclique partition of $$G$$ are denoted by $$\text{s-dim}(G)$$ and $$\text{s-part}(G)$$, respectively. For bipartite domino-free graphs both parameters coincide and can be computed in time $$O(nm)$$.
Reviewer: H.Müller (Jena)

##### MSC:
 05C85 Graph algorithms (graph-theoretic aspects) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C35 Extremal problems in graph theory 68R10 Graph theory (including graph drawing) in computer science 68Q25 Analysis of algorithms and problem complexity
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