RAINBOW CONNECTIVITY OF G(n, p) AT THE CONNECTIVITY THRESHOLD
نویسندگان
چکیده
An edge colored graph G is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this work we study the rainbow connectivity of the binomial graph G = G(n, p) at the connectivity threshold p = logn+ω n where ω = ω(n) → ∞ and ω = o(log n). We prove that the rainbow connectivity of G satisfies rc(G) ∼ max {Z1, diameter(G)} with high probability (whp). Here Z1 is the number of vertices in G whose degree equals 1 and the diameter of G is asymptotically equal to logn log logn , whp.
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