Let \(G(V,E,\gamma)\) be a finite undirected graph. The minimal tree decomposability of the graph \(\tau(G)\) is defined as the minimal natural number \(k\), for which \(G\) is decomposable into \(k\) trees, formally
\[\tau(G):=\min\{k:~G\text{ is decomposable into }k\text{ trees.}\}\]
Corollaries: 1
Corollaries: 1
Proofs: 2 3 4
Theorems: 5
