Decomposition of random graphs into complete bipartite graphs

Abstract

We consider the problem of partitioning the edge set of a graph $G$ into the minimum number $\tau (G)$ of edge-disjoint complete bipartite subgraphs. We show that for a random graph $G$ in $G(n,p)$, for $p$ is a constant no greater than $1/2$, almost surely $\tau (G)$ is between $n-c({\ln }_{1/p}n{)}^{3+\epsilon }$ and $n-2{\ln }_{1/(1-p)}n$ for any positive constants $c$ and $\epsilon$.

References in corpus (1)

• More on the bipartite decomposition of random graphs

Cited by in corpus (1)

• On the decomposition of random hypergraphs