How Do You Spell PATHWIDTH?

Pronunciation: [pˈaθwɪdθ] (IPA)

Pathwidth is a technical term used in graph theory to describe the width of a graph. The spelling of pathwidth [ˈpæθˌwɪdθ] is based on the English spelling system that follows the rules of phonetics. The first syllable is pronounced as /pæθ/ with the "a" pronounced as the "a" in "cat", the "th" as in "bath", and the stress on the first syllable. The second syllable is pronounced as /wɪdθ/ with the "i" pronounced as the "i" in "bit" and the stress on the second syllable.

PATHWIDTH Meaning and Definition

1. Pathwidth is a term used in graph theory, a branch of mathematics that studies the properties and structures of graphs. It refers to a numerical measure of how "narrow" or "wide" a graph is, based on the arrangement of its vertices.

   More specifically, pathwidth is a parameter that quantifies the minimal width of a layout of a graph, where the width is determined by the sequential ordering of the vertices along a path. The pathwidth of a graph represents the smallest width required to layout the graph in such a way that no vertex has more than the specified number of adjacent vertices preceding it along the path.

   Formally, the pathwidth of a graph G is defined as the minimum value of k for which there exists an ordering of the vertices of G such that each vertex has at most k neighbors occurring consecutively in the ordering. The concept of pathwidth is closely related to the notion of tree-width, which is another graph parameter that measures how closely a graph can resemble a tree.

   Pathwidth is a valuable tool in graph theory as it helps in analyzing the complexity of various algorithms and optimization problems on graphs. It has applications in several fields, including computer science, network design, and operations research. By understanding the pathwidth of a graph, researchers can gain insights into its structural properties and develop efficient algorithms for solving graph-based problems.

Etymology of PATHWIDTH

The word "pathwidth" is a combination of two separate terms: "path" and "width".

- "Path" refers to a route or course along which something travels or progresses. It can also be associated with a connected sequence of nodes or vertices in a graph theory context.

- "Width" refers to the measurement of a particular dimension or extent, often associated with the narrower dimension of an object or space.

Thus, when combined, "pathwidth" typically refers to a measurement or quantification of the narrowness or constraint of a path or connected sequence within a graph or network structure.