Cycle interpolation properties of graphs Original Research Article

The length of a set of cycles of a graph G is the sum of the lengths of its cycles. Consider a family An of n-element sets of cycles of G. Let c−(Ag) and c+(An) be the minimum and maximum lengths among all sets of An respectively. We say that Ag has the cycle interpolation property (cip) if for every integer c between c− (An) and c+ (An), there exists in An a set of length c. A graph G has the cycle basis interpolation property (cbip) if the family of all cycle bases of G satisfies the cip. The main result of this paper shows that every maximal outerplanar graph has the cbip.