The Widths of Strict Outerconfluent Graphs

TL;DR

This paper studies a specific graph drawing style called strict outerconfluent, showing that while clique-width can be arbitrarily large, twin-width remains bounded for these graphs.

Contribution

It establishes that strict outerconfluent graphs have unbounded clique-width but bounded twin-width, revealing new structural properties of these graphs.

Findings

Clique-width of strict outerconfluent graphs is unbounded.

Twin-width of these graphs is bounded.

Provides insights into the structural complexity of strict outerconfluent graphs.

Abstract

Strict outerconfluent drawing is a style of graph drawing in which vertices are drawn on the boundary of a disk, adjacencies are indicated by the existence of smooth curves through a system of tracks within the disk, and no two adjacent vertices are connected by more than one of these smooth tracks. We investigate graph width parameters on the graphs that have drawings in this style. We prove that the clique-width of these graphs is unbounded, but their twin-width is bounded.