English

The Langberg-M\'{e}dard Multiple Unicast Conjecture: Stable $3$-Pair Networks

Information Theory 2020-04-21 v3 Combinatorics math.IT

Abstract

The Langberg-M\'{e}dard multiple unicast conjecture claims that for a strongly reachable kk-pair network, there exists a multi-flow with rate (1,1,,1)(1,1,\dots,1). In this paper, we show that the conjecture holds true for {\em stable} 33-pair networks.

Cite

@article{arxiv.2001.02017,
  title  = {The Langberg-M\'{e}dard Multiple Unicast Conjecture: Stable $3$-Pair Networks},
  author = {Kai Cai and Guangyue Han},
  journal= {arXiv preprint arXiv:2001.02017},
  year   = {2020}
}
R2 v1 2026-06-23T13:04:54.540Z