On the Volume of 4-Cycle Trades

Abstract. A 4-cycle trade of volume t corresponds to a simple graph G without isolated vertices, where the edge set can be partitioned into t 4-cycles in at least two different ways such that the two collections of 4-cycles have no 4-cycles in common. The foundation of the trade is v=|V(G)|. This paper determines for which values of t and v there exists a 4-cycle trade of volume t and foundation v.