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- W2205584677 abstract "For an $r$-uniform hypergraph $H$, let $f(H)$ be the minimum number of complete $r$-partite $r$-uniform subhypergraphs of $H$ whose edge sets partition the edge set of $H$. For a graph $G$, $f(G)$ is the bipartition number of $G$ which was introduced by Graham and Pollak in 1971. In 1988, ErdH{o}s conjectured that if $G in G(n,1/2)$, then with high probability $f(G)=n-alpha(G)$, where $alpha(G)$ is the independence number of $G$. This conjecture and related problems have received a lot of attention recently. In this paper, we study the value of $f(H)$ for a typical $r$-uniform hypergraph $H$. More precisely, we prove that if $(log n)^{2.001}/n leq p leq 1/2$ and $H in H^{(r)}(n,p)$, then with high probability $f(H)=(1-pi(K^{(r-1)}_r)+o(1))binom{n}{r-1}$, where $pi(K^{(r-1)}_r)$ is the Tur'an density of $K^{(r-1)}_r$." @default.
- W2205584677 created "2016-06-24" @default.
- W2205584677 creator A5064082253 @default.
- W2205584677 date "2015-10-16" @default.
- W2205584677 modified "2023-09-25" @default.
- W2205584677 title "On the decomposition of random hypergraphs" @default.
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- W2205584677 doi "https://doi.org/10.48550/arxiv.1510.04814" @default.
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