The four <a href="https://en.wikipedia.org/wiki/Forbidden_graph_characterization" class="extiw" title="en:Forbidden graph characterization">minimal forbidden minors</a> for graphs of <a href="https://en.wikipedia.org/wiki/Branchwidth" class="extiw" title="en:Branchwidth">branchwidth</a> three: <i>K</i><sub>5</sub>, the <a href="https://en.wikipedia.org/wiki/Wagner_graph" class="extiw" title="en:Wagner graph">Wagner graph</a>, the graph of the octahedron, and the graph of the cube.
<a href="//commons.wikimedia.org/wiki/User:David_Eppstein" class="mw-redirect" title="User:David Eppstein">David Eppstein</a>
<span class="int-own-work" lang="en">Own work</span>, derived from <a href="//commons.wikimedia.org/wiki/File:Partial_3-tree_forbidden_minors.svg" title="File:Partial 3-tree forbidden minors.svg">File:Partial 3-tree forbidden minors.svg</a>