2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160099We consider network coding rates for directed and undirected $k$-pairs networks. For directed networks, meagerness is known to be an upper bound on network coding rates. We show that network coding rate can be $Θ(|V|)$ multiplicative factor smaller than meagerness. For the undirected case, we show some progress in the direction of the $k$-pairs conjecture.ISIT 2008Information Theorytext