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Yan, Yun-Zhi; Wang, Han-Xing; Wang, Jun; Yin, Xiang-Feng
Statistics & probability letters, 08/2008, Volume: 78, Issue: 11Journal Article
For graphs G n on n vertices and H ( n ) on h n vertices, where h n divides n , an H ( n ) -factor of G n is a spanning subgraph of G n consisting of n / h n vertex disjoint copies of H ( n ) . Our main result has supplied a lower bound (or upper bound) of p in the problem of determining the minimal (or maximal) probability p = p ( n ) , for which almost surely random graph G ( n ; p ) contains an (or contains no) H ( n ) -factor, where H ( n ) satisfies certain conditions. The bound of p for the same problem when H ( n ) is a fixed graph has been studied by Alon and Yuster and by Ruciński and by Krivelevich.
