The biclique partition number 
of a finite simple
graph 
is the minimum number of bicliques whose edge
sets partition the edge
set of 
(Pinto 2014). Such a collection is called a biclique partition. Its members are complete bipartite subgraphs, which need
not be induced subgraphs. They may share vertices,
but each graph edge must occur exactly once.
A biclique cover instead permits repeated coverage of edges. Consequently, the bipartite
dimension is at most the biclique partition number. The inequality can be strict.
For example, the complete graph 
has bipartite dimension
2 and biclique partition number 3 (Pinto 2014).
The Alon-Saks-Seymour conjecture proposed a bound on the chromatic number in terms of the biclique partition number. Huang and Sudakov (2012) disproved that bound.
