Editing Spanning tree (section)

===Fundamental cutsets===
Dual to the notion of a fundamental cycle is the notion of a '''fundamental cutset''' with respect to a given spanning tree. By deleting just one edge of the spanning tree, the vertices are partitioned into two disjoint sets. The fundamental cutset is defined as the set of edges that must be removed from the graph ''G'' to accomplish the same partition. Thus, each spanning tree defines a set of ''V''&nbsp;−&nbsp;1 fundamental cutsets, one for each edge of the spanning tree.<ref>{{harvtxt|Kocay|Kreher|2004}}, pp.&nbsp;67–69.</ref>

The duality between fundamental cutsets and fundamental cycles is established by noting that cycle edges not in the spanning tree can only appear in the cutsets of the other edges in the cycle; and ''vice versa'': edges in a cutset can only appear in those cycles containing the edge corresponding to the cutset. This duality can also be expressed using the theory of [[matroid]]s, according to which a spanning tree is a base of the [[graphic matroid]], a fundamental cycle is the unique circuit within the set formed by adding one element to the base, and fundamental cutsets are defined in the same way from the [[dual matroid]].<ref>{{citation |title=Matroid Theory |volume=3 |series=Oxford [[Graduate Texts in Mathematics]] |first=J. G. |last=Oxley |author-link=James Oxley |publisher=Oxford University Press |year=2006 |isbn=978-0-19-920250-8 |page=141 |url=https://books.google.com/books?id=puKta1Hdz-8C&pg=PA141}}.</ref>