Thinness of product graphs
Abstract
The thinness of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Many NP-complete problems can be solved in polynomial time for graphs with bounded thinness, given a suitable representation of the graph. In this paper we study the thinness and its variations of graph products. We show that the thinness behaves "well" in general for products, in the sense that for most of the graph products defined in the literature, the thinness of the product of two graphs is bounded by a function (typically product or sum) of their thinness, or of the thinness of one of them and the size of the other. We also show for some cases the non-existence of such a function.
Cite
@article{arxiv.2006.16887,
title = {Thinness of product graphs},
author = {Flavia Bonomo-Braberman and Carolina L. Gonzalez and Fabiano S. Oliveira and Moysés S. Sampaio and Jayme L. Szwarcfiter},
journal= {arXiv preprint arXiv:2006.16887},
year = {2023}
}
Comments
45 pages. arXiv admin note: text overlap with arXiv:1704.00379