Bounding the Mim-Width of Hereditary Graph Classes
Abstract
A large number of NP-hard graph problems become polynomial-time solvable on graph classes where the mim-width is bounded and quickly computable. Hence, when solving such problems on special graph classes, it is helpful to know whether the graph class under consideration has bounded mim-width. We first extend the toolkit for proving (un)boundedness of mim-width of graph classes. This enables us to initiate a systematic study into bounding mim-width from the perspective of hereditary graph classes. For a given graph , the class of -free graphs has bounded mim-width if and only if it has bounded clique-width. We show that the same is not true for -free graphs. We find several general classes of -free graphs having unbounded clique-width, but the mim-width is bounded and quickly computable. We also prove a number of new results showing that, for certain and , the class of -free graphs has unbounded mim-width. Combining these with known results, we present summary theorems of the current state of the art for the boundedness of mim-width for -free graphs.
Cite
@article{arxiv.2004.05018,
title = {Bounding the Mim-Width of Hereditary Graph Classes},
author = {Nick Brettell and Jake Horsfield and Andrea Munaro and Giacomo Paesani and Daniel Paulusma},
journal= {arXiv preprint arXiv:2004.05018},
year = {2021}
}