TY - JOUR
AU - Wright, E. M.
AB - THE PROPORTION OF LABELLED BIPARTITE GRAPHS WHICH ARE CONNECTED V. L. KLEE, D. G. LARMAN AND E. M. WRIGHT 1. Introduction An (m, n ; E) graph is a bipartite graph on m labelled red points, n labelled blue points and E lines. Each line joins a red point to a blue point; no two lines join the same pair of points. The numbers m and E depend on n, and m -> oo as n -> oo. We are concerned to find the proportion as n -> oo of (m, n; E) graphs which are connected and, in particular, the threshold (in the sense of Erdos and Renyi [2]) for this property, that is, the interval of E between those values for which almost no (m, n ; E) graphs are connected and those for which almost all are connected. Most practical problems which lead to the study of bipartites concern those in which the points of one part are different in kind from those of the other (for such problems see, for example, [3]). It is therefore natural to study (m, n ; E) bipartites, that is, those in which the m points and the n points 
TI - The Proportion of Labelled Bipartite Graphs which are Connected
JO - Journal of the London Mathematical Society
DO - 10.1112/jlms/s2-24.3.397
DA - 1981-12-01
UR - https://www.deepdyve.com/lp/wiley/the-proportion-of-labelled-bipartite-graphs-which-are-connected-CDIkpDXwrL
SP - 397
EP - 404
VL - s2-24
IS - 3
DP - DeepDyve
ER -