Lower Bounds on the mim-width of Some Graph Classes

TL;DR

This paper establishes tight linear lower bounds on the mim-width for various graph classes, enhancing understanding of their structural complexity and implications for algorithms.

Contribution

It provides the first unconditional linear lower bounds on mim-width for strongly chordal graphs, co-comparability graphs, and circle graphs, refining previous results.

Findings

Linear lower bounds for mim-width in strongly chordal split graphs

Linear lower bounds for mim-width in co-comparability graphs

Linear lower bounds for mim-width in circle graphs

Abstract

mim-width is a recent graph width measure that has seen applications in graph algorithms and problems related to propositional satisfiability. In this paper, we show linear lower bounds for the mim-width of strongly chordal split graphs, co-comparability graphs and circle graphs. This improves and refines lower bounds that were known before, some of them only conditionally. In the case of strongly chordal graphs not even a conditional lower bound was known before. All of the bounds given are optimal up to constants.