Graph compositions and flats of cycle matroids

Abstract

We give an alternative method for counting the number of graph compositions of any graph G. In particular we show that counting the number of graph compositions of a graph G is equivalent to counting the number of flats of its cycle matroid. Then we give one condition for non isomorphic graphs to have the same number of graph compositions.

Quaestiones Mathematicae 32(2009), 523–527