THE /c-CONNECTEDNESS OF BIPARTITE GRAPHS
نویسنده
چکیده
We consider bipartite graphs on m red points and n blue points, where m ^ n, and prove that, for any fixed k, almost all such graphs (labelled or unlabelled) are k-connected as n -» oo, provided m > C logn, where C depends on k. If Tmn is the number of such unlabelled graphs, we show that Tmn ~ 2 /(m \n!). If T'mn is the number of such unlabelled graphs with the colours removed, then T'mn ~ Tmn if m < n and T'nn ~ \Tnn. We deduce that almost all bipartite graphs on p points in all, whether labelled or unlabelled, are fc-connected and so prove a conjecture of Harary and Robinson.
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تاریخ انتشار 2006