Abstract We present a new tool called the "mv-decomposition", and we describe some interesting algorithmic properties about it. We propose an algorithm with a complexity of O(m) to build a mv-decomposition for each bipartite graph. We use this mv-decomposition to propose a solution to the distance-2 broadcast problem in a synchronous multi-hops radio networks where adjacent transmissions are subject to interferences. More precisely, we propose two algorithms of resolution: the first one guarantees a complete distance-2 broadcast scheme using O((log n) 2 ) slots for a time complexity of O(m(log n) 2 ), while the second builds a solution with a minimal number of transmissions for a time complexity of O(m)
