An Algorithm for the Decomposition of Complete Graph into Minimum Number of Edge-disjoint Trees

In this work, we study methodical decomposition of an undirected, unweighted complete graph (K_n of order n, size m) into minimum number of edge-disjoint trees. We find that x, a positive integer, is minimum and x=⌈n/2⌉ as the edge set of K_n is decomposed into edge-disjoint trees of size sequence M = {m_1,m_2,...,m_x} where m_i≤(n-1) and Σ_i=1^x m_i = n(n-1)/2. For decomposing the edge set of K_n into minimum number of edge-disjoint trees, our proposed algorithm takes total O(m) time.