Pathwidth

Summary

In graph theory, a path decomposition of a graph $G$ is, informally, a representation of $G$ as a "thickened" path graph, and the pathwidth of $G$ is a number that measures how much the path was thickened to form $G$. More formally, a path-decomposition is a sequence of subsets of vertices of $G$ such that the endpoints of each edge appear in one of the subsets and such that each vertex appears in a contiguous subsequence of the subsets, and the pathwidth is one less than the size of the largest set in such a decomposition. Pathwidth is also known as interval thickness (one less than the maximum clique size in an interval supergraph of $G$), vertex separation number, or node searching number.