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Bipartite Dimension


The bipartite dimension of a graph G, also called its biclique cover number, is the smallest number of complete bipartite subgraphs whose union contains every graph edge of G. Equivalently, it is the minimum size of an edge cover of G by complete bipartite subgraphs (Fishburn and Hammer 1996).

The bipartite dimension is at most the edge count of G, since each edge is a copy of K_(1,1).


See also

Biclique Cover, Biclique Cover Number, Complete Bipartite Graph, Edge Cover, Graph Edge

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References

Fishburn, P. C. and Hammer, P. L. "Bipartite Dimensions and Bipartite Degrees of Graphs." Disc. Math. 160, 127-148, 1996. https://doi.org/10.1016/0012-365X(95)00154-O.

Cite this as:

Weisstein, Eric W. "Bipartite Dimension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BipartiteDimension.html

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