networks(deprecated)/djspantree - Help

networks

 djspantree
 edge-disjoint spanning trees of a graph

 Calling Sequence djspantree(G)

Parameters

 G - graph or network

Description

 • 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](...).

Examples

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

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{complete}\left(3,4\right):$
 > $\mathrm{addedge}\left(\left\{1,5\right\},G\right):$
 > $\mathrm{djspantree}\left(G\right)$
 ${\mathrm{table}}\left(\left[{1}{=}\left\{{\mathrm{e10}}{,}{\mathrm{e11}}{,}{\mathrm{e12}}{,}{\mathrm{e13}}{,}{\mathrm{e5}}{,}{\mathrm{e7}}\right\}{,}{2}{=}\left\{{\mathrm{e1}}{,}{\mathrm{e2}}{,}{\mathrm{e3}}{,}{\mathrm{e4}}{,}{\mathrm{e6}}{,}{\mathrm{e9}}\right\}{,}{3}{=}\left\{{\mathrm{e8}}\right\}{,}{4}{=}\left\{{}\right\}{,}{5}{=}\left\{{}\right\}{,}{6}{=}\left\{{}\right\}{,}{7}{=}\left\{{}\right\}\right]\right)$ (1)
 > $\mathrm{ends}\left({1}_{},G\right)$
 $\left\{\left\{{1}{,}{5}\right\}{,}\left\{{2}{,}{4}\right\}{,}\left\{{2}{,}{6}\right\}{,}\left\{{3}{,}{5}\right\}{,}\left\{{3}{,}{6}\right\}{,}\left\{{3}{,}{7}\right\}\right\}$ (2)