Important: The networks package has been deprecated.  Use the superseding package GraphTheory instead.

This routine uses Edmonds's matroid partitioning algorithm to find a partition of G into the minimum number of forests. This partitioning works in such a way that as many as possible of the forests in the final partition are spanning trees.

The actual result is returned as a table of edge sets which can be used to induce the appropriate subgraphs.

This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[djspantree](...).

$\mathrm{with}\left(\mathrm{networks}\right)\:$

$G≔\mathrm{complete}\left(3\,4\right)\:$

$\mathrm{addedge}\left(\left\{1\,5\right\}\,G\right)\:$

$\mathrm{djspantree}\left(G\right)$

$table\left(\left[1=\left\{\mathrm{e10}\,\mathrm{e11}\,\mathrm{e12}\,\mathrm{e13}\,\mathrm{e5}\,\mathrm{e7}\right\}\,2=\left\{\mathrm{e1}\,\mathrm{e2}\,\mathrm{e3}\,\mathrm{e4}\,\mathrm{e6}\,\mathrm{e9}\right\}\,3=\left\{\mathrm{e8}\right\}\,4=\varnothing \,5=\varnothing \,6=\varnothing \,7=\varnothing \right]\right)$

$\mathrm{ends}\left(\left[1\right]\,G\right)$

$\left\{\left\{1\,5\right\}\,\left\{2\,4\right\}\,\left\{2\,6\right\}\,\left\{3\,5\right\}\,\left\{3\,6\right\}\,\left\{3\,7\right\}\right\}$