The number of matchings in random regular graphs and bipartite graphs


If 3 ≤ k ≤ (logn) 1 3 and n is even, then the number of 1-factors in random labelled k-regular graphs of order n has expectation ( 2+o(n- 2 3))e 1 4(( k-1)k-1 kk-2) 3n 2 and variance (1+o(n- 1 2))e 1 2(( k-1)k-1 kk-2)ne-( 2k-1 4(k-1)2 k-1 k-2 1 2-1 A similar result is proved for random regular bipartite graphs. © 1986.

Publication Title

Journal of Combinatorial Theory, Series B