Editing Spanning tree (section)

===Spanning forests===
A collection of disjoint (unconnected) trees is described as a ''[[Forest (graph theory) | forest]]''.  A ''spanning forest'' in a graph is a subgraph that is a forest with an additional requirement.  There are two incompatible requirements in use, of which one is relatively rare.

* Almost all graph theory books and articles define a spanning forest as a forest that spans all of the vertices, meaning only that each vertex of the graph is a vertex in the forest. A connected graph may have a disconnected spanning forest, such as the forest with no edges, in which each vertex forms a single-vertex tree.<ref name="pearls">{{citation |title=Pearls in Graph Theory: A Comprehensive Introduction|title-link= Pearls in Graph Theory
 |last1=Hartsfield |first1=Nora |last2=Ringel |first2=Gerhard |author2-link=Gerhard Ringel |publisher=Courier Dover Publications |year=2003 |isbn=978-0-486-43232-8 |at=[https://books.google.com/books?id=R6pq0fbQG0QC&pg=PA100 p. 100]}}.</ref><ref>{{citation |title=Combinatorics: Topics, Techniques, Algorithms |first=Peter J. |last=Cameron |author-link=Peter Cameron (mathematician) |publisher=Cambridge University Press |year=1994 |isbn=978-0-521-45761-3 |page=163 |url=https://books.google.com/books?id=_aJIKWcifDwC&pg=PA163}}.</ref>

* A few graph theory authors define a spanning forest to be a maximal acyclic subgraph of the given graph, or equivalently a subgraph consisting of a spanning tree in each [[Connected component (graph theory)|connected component]] of the graph.<ref>{{citation |title=Modern Graph Theory |volume=184 |series=Graduate Texts in Mathematics |first=Béla |last=Bollobás |author-link=Béla Bollobás |publisher=Springer |year=1998 |isbn=978-0-387-98488-9 |page=350 |url=https://books.google.com/books?id=SbZKSZ-1qrwC&pg=PA350}}; {{citation |title=LEDA: A Platform for Combinatorial and Geometric Computing |first=Kurt |last=Mehlhorn |author-link=Kurt Mehlhorn |publisher=Cambridge University Press |year=1999 |isbn=978-0-521-56329-1 |page=260 |url=https://books.google.com/books?id=Q2aXZl3fgvMC&pg=PA260}}.</ref>

To avoid confusion between these two definitions, {{harvtxt|Gross|Yellen|2005}} suggest the term "full spanning forest" for a spanning forest with the same number of components as the given graph (i.e., a maximal forest), while {{harvtxt|Bondy|Murty|2008}} instead call this kind of forest a "maximal spanning forest" (which is redundant, as a maximal forest necessarily contains every vertex).<ref>{{citation |title=Graph Theory and Its Applications |edition=2nd |first1=Jonathan L. |last1=Gross |first2=Jay |last2=Yellen |publisher=CRC Press |year=2005 |isbn=978-1-58488-505-4 |page=168 |url=https://books.google.com/books?id=-7Q_POGh-2cC&pg=PA168}}; {{citation |title=Graph Theory |volume=244 |series=Graduate Texts in Mathematics |first1=J. A. |last1=Bondy |first2=U. S. R. |last2=Murty |publisher=Springer |year=2008 |isbn=978-1-84628-970-5 |page=578 |url=https://books.google.com/books?id=V0gUTxkOSboC&pg=PA578}}.</ref>