File talk:Bipartite-dimension-biclique-cover.svg

Each colour is a complete bipartite graph on 2+3 vertices. So four of the 20 edges are shown in two different colours. I wonder why. Maproom (talk) 14:59, 7 May 2013 (UTC)[reply]

Are you wondering about the asymmetry in the edges that receive more than one color?

If I remember correctly, I tried to minimize the amount of bicolored edges when I drew the image. This would hopefully make it easier to grasp the concept of a biclique cover for most people.

There is a canonical construction of a minimal biclique edge cover for crown graphs. If I remember correctly, the construction shows a more symmetric pattern, but more edges will receive more than one color. The construction is cited (but not explained) in the article on bipartite dimension.

And, for the record: You cannot cover the edge set of this graph with fewer bicliques. Also, if you want to partition the edge set into bicliques (i.e. every edge receives a unique color), then you will need more bicliques. Hermel (talk) 21:50, 12 May 2013 (UTC)[reply]