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- W3006476046 abstract "An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph G, denoted by cfc(G), is the smallest number of colors needed in order to make G conflict-free connected. In this paper, we show that almost all graphs have the conflict-free connection number 2. More precisely, let G(n,p) denote the Erdős–Rényi random graph model, in which each of the n2 pairs of vertices appears as an edge with probability p independent from other pairs. We prove that for sufficiently large n, cfc(G(n,p))≤2 if p≥logn+α(n)n, where α(n)→∞. This means that as soon as G(n,p) becomes connected with high probability, cfc(G(n,p))≤2." @default.
- W3006476046 created "2020-02-24" @default.
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- W3006476046 date "2020-09-01" @default.
- W3006476046 modified "2023-10-16" @default.
- W3006476046 title "Conflict-free connection number of random graphs" @default.
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- W3006476046 doi "https://doi.org/10.1016/j.dam.2020.01.034" @default.
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