On the volume of 4-cycle trades

Bryant, Darryn; Grannell, Mike; Griggs, Terry and Maenhaut, Barbara (2003). On the volume of 4-cycle trades. Graphs and Combinatorics, 19(1) pp. 53–63.

DOI: https://doi.org/10.1007/s00373-002-0484-x

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.