Threshold Functions for H-factors
نویسندگان
چکیده
Let H be a graph on h vertices, and let G be a graph on n vertices. An H-factor of G is a spanning subgraph of G consisting of n/h vertex disjoint copies of H. The fractional arboricity of H is a(H) = max{ |E ′| |V ′|−1}, where the maximum is taken over all subgraphs (V ′, E′) of H with |V ′| > 1. Let δ(H) denote the minimum degree of a vertex of H. It is shown that if δ(H) < a(H) then n−1/a(H) is a sharp threshold function for the property that the random graph G(n, p) contains an H-factor. I.e., there are two positive constants c and C so that for p(n) = cn−1/a(H), almost surely G(n, p(n)) does not have an H-factor, whereas for p(n) = Cn−1/a(H), almost surely G(n, p(n)) contains an H-factor (provided h divides n). A special case of this answers a problem of Erdös. ∗Research supported in part by a United States Israeli BSF grant
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 2 شماره
صفحات -
تاریخ انتشار 1993