Covering of graphs by complete bipartite subgraphs; Complexity of 0–1 matrices


We prove that the edge set of an arbitrary simple graphG onn vertices can be covered by at mostn−[log2 n]+1 complete bipartite subgraphs ofG. If the weight of a subgraph is the number of its vertices, then there always exists a cover with total weightc(n 2/logn) and this bound is sharp apart from a constant factor. Our result answers a problem of T. G. Tarján.

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Dedicated to Paul Erdős on his seventieth birthday

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Tuza, Z. Covering of graphs by complete bipartite subgraphs; Complexity of 0–1 matrices. Combinatorica 4, 111–116 (1984).

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AMS subject classification (1980)

  • 05 C 35
  • 15 A 99