Rank-width: Algorithmic and structural results

TL;DR

This survey reviews the current state of research on rank-width, a graph parameter that measures how well a graph can be decomposed into a tree-like structure, highlighting algorithmic and structural insights.

Contribution

It compiles and summarizes known algorithmic and structural results related to rank-width, providing a comprehensive overview of the field.

Findings

Rank-width can be computed efficiently for certain graph classes.

Graphs with bounded rank-width have polynomial-time algorithms for various problems.

Structural properties of graphs with bounded rank-width are well-understood.

Abstract

Rank-width is a width parameter of graphs describing whether it is possible to decompose a graph into a tree-like structure by `simple' cuts. This survey aims to summarize known algorithmic and structural results on rank-width of graphs.