Minimum degree spanning tree

In graph theory, for a connected graph $G$, a spanning tree $T$ is a subgraph of $G$ with the least number of edges that still spans $G$. A number of properties can be proved about $T$. $T$ is acyclic, has ($|V|-1$) edges where $V$ is the number of vertices in $G$ etc.

A minimum degree spanning tree $T'$ is a spanning tree which has the least maximum degree. The vertex of maximum degree in $T'$ is the least among all possible spanning trees of $G$.

Finding minimum degree spanning tree is NP hard, but a local search algorithm can give a tree which its maximum degree is at most the maximum degree of optimal tree plus one.

See Degree-Constrained Spanning Tree.