Six-cycle trades and a lower bound on the trade volumes of weakly connected graphs - Lefevre, James G. (Utilitas Mathematica, 2007)
A C6-trade consists of two disjoint decompositions of some simple graph H into copies of C6. The number of vertices of H is referred to as the foundation of the trade, while the number of copies of C 6 in each of the decompositions is called the volume of the trade. We determine the values of v and s for which there exists a C6-trade of volume s and foundation v. We also present a more general result giving a lower bound for the trade volumes of various weakly connected graphs (including paths and cycles).