Treewidth is a graph parameter which measures how close the graph is to a tree (smaller is better). Many problems can be solved more efficiently on graphs with bounded treewidth, using dynamic programming.
Treewidth is a graph parameter which measures how close the graph is to a tree. For example, forests have treewidth 1, and series-parallel graphs have treewidth 2.
A graph $G$ has treewidth $k$ if there is a tree $T$ whose vertices are labelled by sets of $k+1$ vertices of $G$ such that (i) every edge of $G$ is covered by one of the sets and (ii) for every vertex $v$ of $G$, the vertices of $T$ whose sets contain $v$ are connected.
Many algorithmic tasks can be solved efficiently on graphs of bounded treewidth using dynamic programming, by extending algorithms that work on trees. Consequently, such tasks are fixed-parameter tractable when parametrized by treewidth.
Treewidth is one of a family of related parameters, such as pathwidth (in which $T$ is restricted to be a path).
